Relevant bibliographies by topics / Symbolic dynamics. Topological dynamics

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Academic literature on the topic 'Symbolic dynamics. Topological dynamics'

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Published: 4 June 2021
Last updated: 16 February 2022

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Journal articles on the topic "Symbolic dynamics. Topological dynamics"

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Morales, C. A., and Jumi Oh. "Symbolic topological dynamics in the circle." Proceedings of the American Mathematical Society 147, no. 8 (March 26, 2019): 3413–24. http://dx.doi.org/10.1090/proc/14472.

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Galias, Zbigniew. "Automatized Search for Complex Symbolic Dynamics with Applications in the Analysis of a Simple Memristor Circuit." International Journal of Bifurcation and Chaos 24, no. 07 (July 2014): 1450104. http://dx.doi.org/10.1142/s0218127414501041.

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An automatized method to search for complex symbolic dynamics is proposed. The method can be used to show that a given dynamical system is chaotic in the topological sense. Application of this method in the analysis of a third-order memristor circuit is presented. Several examples of symbolic dynamics are constructed. Positive lower bounds for the topological entropy of an associated return map are found showing that the system is chaotic in the topological sense.
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Correia Ramos, Carlos. "Kinematics in Biology: Symbolic Dynamics Approach." Mathematics 8, no. 3 (March 4, 2020): 339. http://dx.doi.org/10.3390/math8030339.

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Motion in biology is studied through a descriptive geometrical method. We consider a deterministic discrete dynamical system used to simulate and classify a variety of types of movements which can be seen as templates and building blocks of more complex trajectories. The dynamical system is determined by the iteration of a bimodal interval map dependent on two parameters, up to scaling, generalizing a previous work. The characterization of the trajectories uses the classifying tools from symbolic dynamics—kneading sequences, topological entropy and growth number. We consider also the isentropic trajectories, trajectories with constant topological entropy, which are related with the possible existence of a constant drift. We introduce the concepts of pure and mixed bimodal trajectories which give much more flexibility to the model, maintaining it simple. We discuss several procedures that may allow the use of the model to characterize empirical data.
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Xu, Haiyun, Fangyue Chen, and Weifeng Jin. "Topological Conjugacy Classification of Elementary Cellular Automata with Majority Memory." International Journal of Bifurcation and Chaos 27, no. 14 (December 30, 2017): 1750217. http://dx.doi.org/10.1142/s0218127417502170.

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The topological conjugacy classification of elementary cellular automata with majority memory (ECAMs) is studied under the framework of symbolic dynamics. In the light of the conventional symbolic sequence space, the compact symbolic vector space is identified with a feasible metric and topology. A slight change is introduced to present that all global maps of ECAMs are continuous functions, thereafter generating the compact dynamical systems. By exploiting two fundamental homeomorphisms in symbolic vector space, all ECAMs are furthermore grouped into 88 equivalence classes in the sense that different mappings in the same global equivalence are mutually topologically conjugate.
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Ramos, Carlos. "Animal movement: symbolic dynamics and topological classification." Mathematical Biosciences and Engineering 16, no. 5 (2019): 5464–89. http://dx.doi.org/10.3934/mbe.2019272.

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Peng, Shou-Li, and Xu-Sheng Zhang. "Second topological conjugate transformation in symbolic dynamics." Physical Review E 57, no. 5 (May 1, 1998): 5311–24. http://dx.doi.org/10.1103/physreve.57.5311.

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Pei, Yangjun, Qi Han, Chao Liu, Dedong Tang, and Junjian Huang. "Chaotic Behaviors of Symbolic Dynamics about Rule 58 in Cellular Automata." Mathematical Problems in Engineering 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/834268.

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The complex dynamical behaviors of rule 58 in cellular automata are investigated from the viewpoint of symbolic dynamics. The rule is Bernoulliστ-shift rule, which is members of Wolfram’s class II, and it was said to be simple as periodic before. It is worthwhile to study dynamical behaviors of rule 58 and whether it possesses chaotic attractors or not. It is shown that there exist two Bernoulli-measure attractors of rule 58. The dynamical properties of topological entropy and topological mixing of rule 58 are exploited on these two subsystems. According to corresponding strongly connected graph of transition matrices of determinative block systems, we divide determinative block systems into two subsets. In addition, it is shown that rule 58 possesses rich and complicated dynamical behaviors in the space of bi-infinite sequences. Furthermore, we prove that four rules of global equivalence classε43of CA are topologically conjugate. We use diagrams to explain the attractors of rule 58, where characteristic function is used to describe that some points fall into Bernoulli-shift map after several times iterations, and we find that these attractors are not global attractors. The Lameray diagram is used to show clearly the iterative process of an attractor.
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Chen, Fangyue, Bo Chen, Junbiao Guan, and Weifeng Jin. "A Symbolic Dynamics Perspective of Conway’s Game of Life." International Journal of Bifurcation and Chaos 26, no. 02 (February 2016): 1650035. http://dx.doi.org/10.1142/s0218127416500358.

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An interesting question is whether the intrinsic complexity of the gliders in [Formula: see text]-dimensional cellular automata could be quantitatively analyzed in rigorously mathematical sense. In this paper, by introducing the [Formula: see text]-dimensional symbolic space, some fundamental dynamical properties of [Formula: see text]-dimensional shift map are explored in a subtle way. The purpose of this article is to present an accurate characterization of complex symbolic dynamics of gliders in Conway’s game of life. A series of dynamical properties of gliders on their concrete subsystems are investigated by means of the directed graph representation and transition matrix. More specifically, the gliders here are topologically mixing and possess the positive topological entropy on their subsystems. Finally, it is worth mentioning that the method presented in this paper is also applicable to other gliders in different [Formula: see text] dimensions.
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COLLINS, PIETER. "SYMBOLIC DYNAMICS FROM HOMOCLINIC TANGLES." International Journal of Bifurcation and Chaos 12, no. 03 (March 2002): 605–17. http://dx.doi.org/10.1142/s0218127402004565.

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We present a method for finding symbolic dynamics for a planar diffeomorphism with a homoclinic tangle. The method only requires a finite piece of tangle, which can be computed with available numerical techniques. The symbol space is naturally given by components of the complement of the stable and unstable manifolds. The shift map defining the dynamics is a factor of a subshift of finite type, and is obtained from a graph related to the tangle. The entropy of this shift map is a lower bound for the topological entropy of the planar diffeomorphism. We give examples arising from the Hénon family.
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HOCHMAN, MICHAEL. "Genericity in topological dynamics." Ergodic Theory and Dynamical Systems 28, no. 1 (February 2008): 125–65. http://dx.doi.org/10.1017/s0143385707000521.

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AbstractWe study genericity of dynamical properties in the space of homeomorphisms of the Cantor set and in the space of subshifts of a suitably large shift space. These rather different settings are related by a Glasner–King type correspondence: genericity in one is equivalent to genericity in the other. By applying symbolic techniques in the shift-space model we derive new results about genericity of dynamical properties for transitive and totally transitive homeomorphisms of the Cantor set. We show that the isomorphism class of the universal odometer is generic in the space of transitive systems. On the other hand, the space of totally transitive systems displays much more varied dynamics. In particular, we show that in this space the isomorphism class of every Cantor system without periodic points is dense and the following properties are generic: minimality, zero entropy, disjointness from a fixed totally transitive system, weak mixing, strong mixing and minimal self joinings. The latter two stand in striking contrast to the situation in the measure-preserving category. We also prove a correspondence between genericity of dynamical properties in the measure-preserving category and genericity of systems supporting an invariant measure with the same property.
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Dissertations / Theses on the topic "Symbolic dynamics. Topological dynamics"

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Seward, Brandon Michael Gao Su. "On the density of minimal free subflows of general symbolic flows." [Denton, Tex.] : University of North Texas, 2009. http://digital.library.unt.edu/permalink/meta-dc-11009.

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Cecchi, Bernales Paulina Alejandra. "Invariant measures in symbolic dynamics : a topological, combinatorial and geometrical approach." Thesis, Sorbonne Paris Cité, 2019. https://theses.md.univ-paris-diderot.fr/CECCHI-BERNALES_Paulina_2_complete_20190626.pdf.

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Dans ce travail nous étudions quelques propriétés des systèmes symboliques, avec un accent particulier mis sur le rôle joué par les mesures invariantes de tels systèmes. Nous nous attachons à l'étude des mesures invariantes d'un point de vue topologique, combinatoire et géométrique. Du point de vue topologique, nous nous concentrons sur le problème de l'équivalence orbitale et l'équivalence orbitale forte entre des systèmes dynamiques donnés par des actions minimales de Z, par l'étude d'un invariant algébrique, à savoir, le groupe de dimension dynamique. Notre travail donne une description du groupe de dimension dynamique pour deux classes particulières de sous-shifts : les sous-shifts S-adiques et les sous-shifts dendriques. Du point de vue combinatoire, nous nous intéressons au problème de l'équilibre des sous-shifts minimaux et uniquement ergodiques donnés par des actions de Z. Nous étudions le comportement concernant l'équilibre pour des sous-shifts substitutifs, S-adiques et dendriques. Nous établissons des conditions nécessaires pour qu'un sous-shift substitutif minimal avec des fréquences rationnelles soit équilibré par rapport à ses facteurs, en obtenant comme corollaire le déséquilibre des facteurs de longueur supérieure à 2 dans le sous-shift engendré par la substitution de Thue-Morse. Enfin, du point de vue géométrique, nous étudions le problème de réalisation des simplexes de Choquet comme des ensembles de mesures de probabilité invariantes associés à des systèmes donnés par des actions minimales des groupes moyennables sur l'ensemble de Cantor. Nous introduisons la notion de groupe moyennable congruent-monopavable, nous montrons que tout groupe moyennable virtuellement nilpotent est congruent-monopavable, et que pour un group discret infini G avec cette propriété, tout simplexe de Choquet peut s'obtenir comme l'ensemble des mesures invariantes d'un G-sous-shift minimal
In this work we study some dynamical properties of symbolic dynamical systems, with particular emphasis on the role played by the invariant probability measures of such systems. We approach the study of the set of invariant measures from a topological, combinatorial and geometrical point of view. From a topological point of view, we focus on the problem of orbit equivalence and strong orbit equivalence between dynamical systems given by minimal actions of Z, through the study of an algebraic invariant, namely the dynamical dimension group. Our work presents a description of the dynamical dimension group for two particular classes of subshifts: S-adic subshifts and dendric subshifts. From a combinatorial point of view, we are interested in the problem of balance in minimal uniquely ergodic systems given by actions of Z. We investigate the behavior regarding balance for substitutive, S-adic and dendric subshifts. We give necessary conditions for a minimal substitutive system with rational frequencies to be balanced on its factors, obtaining as a corollary the unbalance in the factors of length at least 2 in the subshift generated by the Thue-Morse sequence. Finally, from the geometrical point of view, we investigate the problem of realization of Choquet simplices as sets of invariant probability measures associated to systems given by minimal actions of amenable groups on the Cantor set. We introduce the notion of congruent monotileable amenable group, we prove that every virtually nilpotent amenable group is congruent monotileable, and we show that for a discrete infinite group G with this property, every Choquet simplex can be obtained as the set of invariant measures of a minimal G-subshift
En este trabajo estudiamos algunas propiedades dinamicas de sistemas simbolicos, con especial enfasis en el rol que juegan las medidas de probabilidad invariantes de tales sistemas. Nuestra aproximacion al estudio de las medidas invariantes se realiza desde tres angulos: topologico, combinatorio y geometrico. Desde el punto de vista topologico, nos enfocamos en el problema de la equivalencia orbital y equivalencia orbital fuerte entre sistemas dinamicos dados por acciones minimales de Z, a traves del estudio de un invariante algebraico, a saber, el grupo de dimension dinamico. Nuestro trabajo presenta una descripcion del grupo de dimension dinamico para dos clases particulares de subshifts minimales: los subshifts S-adicos y los subshifts dendricos. Desde el punto de vista combinatorio, nos interesamos en el problema del equilibrio en subshifts minimales y unicamente ergodicos dados por acciones de Z. Investigamos el comportamiento en relacional equilibrio para subshifts substitutivos, S-adicos y dendricos. Establecemos condiciones necesarias para que un subshift substitutivo minimal con frecuencias racionales sea equilibrado en sus factores, obteniendo como corolario el desequilibrio en los factores de largo mayor o igual a 2 en el subshift generado por la substitucion de Thue–Morse. Finalmente, desde el punto de vista geometrico, investigamos la posibilidad de realizar sımplices de Choquet como conjuntos de medidas de probabilidad invariantes asociados a sistemas dados por acciones minimales de grupos promediables sobre el Cantor. Introducimos la nocion de grupo promediable congruente-monoembaldosable, probamos que todo grupo promediable virtualmente nilpotentees congruente-monoembaldosable, y mostramos que para un grupo discreto e infinito G con estapropiedad, todo sımplice de Choquet puede obtenerse como el conjunto de medidas invariantes de un G-subshift minimal
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Alcaraz, Barrera Rafael. "Topological and symbolic dynamics of the doubling map with a hole." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/topological-and-symbolic-dynamics-of-the-doubling-map-with-a-hole(b6f17b43-5285-4e35-883a-baf4708993bc).html.

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This work motivates the study of open dynamical systems corresponding to the doubling map. In particular, the dynamical properties of the attractor of the doubling map when a symmetric, centred open interval is removed are studied. Using the arithmetical properties of the binary expansion of the points on the boundary of the removed interval, we study properties such as topological transitivity, the specification property and intrinsic ergodicity. The properties of the function that associates to each hole $(a,b)$ the topological entropy of the attractor of the considered dynamical system are also shown. For these purposes, a subshift corresponding to an element of the lexicographic world is associated to each attractor and the mentioned properties are studied symbolically.
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Pavlov, Ronald Lee. "Some results on recurrence and entropy." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1180454690.

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Seward, Brandon Michael. "On the density of minimal free subflows of general symbolic flows." Thesis, University of North Texas, 2009. https://digital.library.unt.edu/ark:/67531/metadc11009/.

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This paper studies symbolic dynamical systems {0, 1}G, where G is a countably infinite group, {0, 1}G has the product topology, and G acts on {0, 1}G by shifts. It is proven that for every countably infinite group G the union of the minimal free subflows of {0, 1}G is dense. In fact, a stronger result is obtained which states that if G is a countably infinite group and U is an open subset of {0, 1}G, then there is a collection of size continuum consisting of pairwise disjoint minimal free subflows intersecting U.
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Epperlein, Jeremias. "Topological Conjugacies Between Cellular Automata." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-231823.

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We study cellular automata as discrete dynamical systems and in particular investigate under which conditions two cellular automata are topologically conjugate. Based on work of McKinsey, Tarski, Pierce and Head we introduce derivative algebras to study the topological structure of sofic shifts in dimension one. This allows us to classify periodic cellular automata on sofic shifts up to topological conjugacy based on the structure of their periodic points. We also get new conjugacy invariants in the general case. Based on a construction by Hanf and Halmos, we construct a pair of non-homeomorphic subshifts whose disjoint sums with themselves are homeomorphic. From this we can construct two cellular automata on homeomorphic state spaces for which all points have minimal period two, which are, however, not topologically conjugate. We apply our methods to classify the 256 elementary cellular automata with radius one over the binary alphabet up to topological conjugacy. By means of linear algebra over the field with two elements and identities between Fibonacci-polynomials we show that every conjugacy between rule 90 and rule 150 cannot have only a finite number of local rules. Finally, we look at the sequences of finite dynamical systems obtained by restricting cellular automata to spatially periodic points. If these sequences are termwise conjugate, we call the cellular automata conjugate on all tori. We then study the invariants under this notion of isomorphism. By means of an appropriately defined entropy, we can show that surjectivity is such an invariant.
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Donoso, Sebastian Andres. "Contributions to ergodic theory and topological dynamics : cube structures and automorphisms." Thesis, Paris Est, 2015. http://www.theses.fr/2015PEST1007/document.

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Cette thèse est consacrée à l'étude des différents problèmes liés aux structures des cubes , en théorie ergodique et en dynamique topologique. Elle est composée de six chapitres. La présentation générale nous permet de présenter certains résultats généraux en théorie ergodique et dynamique topologique. Ces résultats, qui sont associés d'une certaine façon aux structures des cubes, sont la motivation principale de cette thèse. Nous commençons par les structures de cube introduites en théorie ergodique par Host et Kra (2005) pour prouver la convergence dans $L^2 $ de moyennes ergodiques multiples. Ensuite, nous présentons la notion correspondante en dynamique topologique. Cette théorie, développée par Host, Kra et Maass (2010), offre des outils pour comprendre la structure topologique des systèmes dynamiques topologiques. En dernier lieu, nous présentons les principales implications et extensions dérivées de l'étude de ces structures. Ceci nous permet de motiver les nouveaux objets introduits dans la présente thèse, afin d'expliquer l'objet de notre contribution. Dans le Chapitre 1, nous nous attachons au contexte général en théorie ergodique et dynamique topologique, en mettant l'accent sur l'étude de certains facteurs spéciaux. Les Chapitres 2, 3, 4 et 5 nous permettent de développer les contributions de cette thèse. Chaque chapitre est consacré à un thème particulier et aux questions qui s'y rapportent, en théorie ergodique ou en dynamique topologique, et est associé à un article scientifique. Les structures de cube mentionnées plus haut sont toutes définies pour un espace muni d'une unique transformation. Dans le Chapitre 2, nous introduisons une nouvelle structure de cube liée à l'action de deux transformations S et T qui commutent sur un espace métrique compact X. Nous étudions les propriétés topologiques et dynamiques de cette structure et nous l'utilisons pour caractériser les systèmes qui sont des produits ou des facteurs de produits. Nous présentons également plusieurs applications, comme la construction des facteurs spéciaux. Le Chapitre 3 utilise la nouvelle structure de cube définie dans le Chapitre 2 dans une question de théorie ergodique mesurée. Nous montrons la convergence ponctuelle d'une moyenne cubique dans un système muni deux transformations qui commutent. Dans le Chapitre 4, nous étudions le semigroupe enveloppant d'une classe très importante des systèmes dynamiques, les nilsystèmes. Nous utilisons les structures des cubes pour montrer des liens entre propriétés algébriques du semigroupe enveloppant et les propriétés topologiques et dynamiques du système. En particulier, nous caractérisons les nilsystèmes d'ordre 2 par une propriété portant sur leur semigroupe enveloppant. Dans le Chapitre 5, nous étudions les groupes d'automorphismes des espaces symboliques unidimensionnels et bidimensionnels. Nous considérons en premier lieu des systèmes symboliques de faible complexité et utilisons des facteurs spéciaux, dont certains liés aux structures de cube, pour étudier le groupe de leurs automorphismes. Notre résultat principal indique que, pour un système minimal de complexité sous-linéaire, le groupe d'automorphismes est engendré par l'action du shift et un ensemble fini. Par ailleurs, en utilisant les facteurs associés aux structures de cube introduites dans le Chapitre 2, nous étudions le groupe d'automorphismes d'un système de pavages représentatif. La bibliographie, commune à l'ensemble de la thèse, se trouve en fin document
This thesis is devoted to the study of different problems in ergodic theory and topological dynamics related to og cube structures fg. It consists of six chapters. In the General Presentation we review some general results in ergodic theory and topological dynamics associated in some way to cubes structures which motivates this thesis. We start by the cube structures introduced in ergodic theory by Host and Kra (2005) to prove the convergence in $L^2$ of multiple ergodic averages. Then we present its extension to topological dynamics developed by Host, Kra and Maass (2010), which gives tools to understand the topological structure of topological dynamical systems. Finally we present the main implications and extensions derived of studying these structures, we motivate the new objects introduced in the thesis and sketch out our contributions. In Chapter 1 we give a general background in ergodic theory and topological dynamics given emphasis to the treatment of special factors. % We give basic definitions and describe special factors associated to a From Chapter 2 to Chapter 5 we develop the contributions of this thesis. Each one is devoted to a different topic and related questions, both in ergodic theory and topological dynamics. Each one is associated to a scientific article. In Chapter 2 we introduce a novel cube structure to study the actions of two commuting transformations $S$ and $T$ on a compact metric space $X$. In the same chapter we study the topological and dynamical properties of such structure and we use it to characterize products systems and their factors. We also provide some applications, like the construction of special factors. In the same topic, in Chapter 3 we use the new cube structure to prove the pointwise convergence of a cubic average in a system with two commuting transformations. In Chapter 4, we study the enveloping semigroup of a very important class of dynamical systems, the nilsystems. We use cube structures to show connexions between algebraic properties of the enveloping semigroup and the geometry and dynamics of the system. In particular, we characterize nilsystems of order 2 by its enveloping semigroup. In Chapter 5 we study automorphism groups of one-dimensional and two-dimensional symbolic spaces. First, we consider low complexity symbolic systems and use special factors, some related to the introduced cube structures, to study the group of automorphisms. Our main result states that for minimal systems with sublinear complexity such groups are spanned by the shift action and a finite set. Also, using factors associated to the cube structures introduced in Chapter 2 we study the automorphism group of a representative tiling system. The bibliography is defer to the end of this document
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Kenny, Robert. "Orbit complexity and computable Markov partitions." University of Western Australia. School of Mathematics and Statistics, 2008. http://theses.library.uwa.edu.au/adt-WU2008.0231.

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Markov partitions provide a 'good' mechanism of symbolic dynamics for uniformly hyperbolic systems, forming the classical foundation for the thermodynamic formalism in this setting, and remaining useful in the modern theory. Usually, however, one takes Bowen's 1970's general construction for granted, or restricts to cases with simpler geometry (as on surfaces) or more algebraic structure. This thesis examines several questions on the algorithmic content of (topological) Markov partitions, starting with the pointwise, entropy-like, topological conjugacy invariant known as orbit complexity. The relation between orbit complexity de nitions of Brudno and Galatolo is examined in general compact spaces, and used in Theorem 2.0.9 to bound the decrease in some of these quantities under semiconjugacy. A corollary, and a pointwise analogue of facts about metric entropy, is that any Markov partition produces symbolic dynamics matching the original orbit complexity at each point. A Lebesgue-typical value for orbit complexity near a hyperbolic attractor is also established (with some use of Brin-Katok local entropy), and is technically distinct from typicality statements discussed by Galatolo, Bonanno and their co-authors. Both our results are proved adapting classical arguments of Bowen for entropy. Chapters 3 and onwards consider the axiomatisation and computable construction of Markov partitions. We propose a framework of 'abstract local product structures'
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Maranhão, Dariel Mazzoni. "Estudo topológico de órbitas periódicas no circuito experimental de Chua." Universidade de São Paulo, 2006. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-24032007-174511/.

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Estudamos o comportamento dinâmico de séries temporais experimentais obtidas de um circuito de Chua quando dois parâmetros de controle, $Delta R_1$ e $Delta R_2$, são variados.Investigamos os comportamentos caótico e periódico, analisando as séries temporais ao redor e no interior de duas janelas periódicas presentes no espaço de parâmetros $(Delta R_1,Delta R_2)$ do circuito. Na vizinhança da janela de período três, analisamos como a dinâmica simbólica se altera quando construída em diferentes seções de Poincaré de um mesmo atrator, e investigamos a dimensão dos mapas de retorno, uni ou bidimensional, para diferentes atratores caóticos presentes nessa região do espaço de parâmetros. Ainda nessa vizinhança, empregamos técnicas de caracterização topológica para confirmar a existência de fibras caóticas, que são curvas de codimensão um no espaço de parâmetros onde as propriedades caóticas dos atratores são preservadas.Ao redor da janela de período quatro, investigamos a transição entre os três comportamentos caóticos para os quais construímos os respectivos moldes topológicos. Propusemos também um molde topológico para o regime caótico após a crise por fusão ocorrer no circuito. Finalizando, investigamos as bifurcações e a estrutura topológica das órbitas periódicas que formam as janelas de período três e de período quatro, construindo um espaço de parâmetros topológico, baseado em um mapa bi-modal, para descrever as duas janela periódicas.
We have studied the dynamical behavior of experimental time series obtained from a Chua's circuit by variation of two parameter control, $Delta R_1$ and $Delta R_2$. We investigated the chaotic and periodic behaviors of the circuit, analyzing temporal series around and inside of two periodic windows in the two-parameter space $(Delta R_1,Delta R_2)$. In the period-three window neighborhood, we analyzed how the symbolic dynamics changes when it is built by different Poincaré sections of an attractor, and we studied the dimension of return map, one- or two-dimensional, for many chaotic attractors in this region of the parameter space. In this neighborhood, we also applied topological techniques to confirm the existence of chaotic fibers: codimension one curves where the chaotic properties of the attractors remain unchanged in the two-parameter space.Around the period-four window, we investigated, by template analysis, the transition between three chaotic attractors found in the Chua's circuit. We proposed a template for chaotic regime of the circuit after merge-crisis. Finally, we investigated the bifurcations and topological structure of periodic orbits in period-three and period-four windows and also proposed a topological parameter space, based in a bimodal map model, that describe these two periodic windows.
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Baptista, Diogo Pedro Ferreira Nascimento. "Iteradas de aplicações do plano no plano." Doctoral thesis, Universidade de Évora, 2008. http://hdl.handle.net/10174/12257.

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Neste trabalho estudamos as iteradas de aplicações do plano no plano. Usando as técnicas da dinâmica simbólica em aplicações do plano no plano, tendo sempre por base a teoria de amassamento de Milnor e Thurston e o formalismo da dinâmica simbólica desenvolvido por Sousa Ramos, abordamos diferentes aspectos qualitativos da dinâmica das aplicações de Lozi. Assim, através da dinâmica simbólica introduzida por Yutaka Ishii, começamos por refor-mular a fronteira do espaço dos parâmetros correspondente às aplicações de Lozi equivalentes à ferradura de Smale. No seguimento, apresentamos um método que permite a construção da bacia de atracção para o atractor de uma qualquer aplicação de Lozi. Ainda usando a dinâmica simbólica para as aplicações de Lozi, apresentamos um método que fazendo uso de expansões em fracções contínuas, nos permite calcular o maior dos expoentes de Lyapunov de uma aplicação de Lozi. Com a introdução do conceito de ponto crítico e subsequentemente de sequência de amassamento para as aplicações de Lozi, partimos para uma a construção de uma partição de Markov do seu espaço de fases. Desse modo, é possível a caracterização completa do espaço dos parâmetros através da introdução do conceito de curva de amassamento, que mostramos serem curvas isentrópicas. Consequentemente, obtemos a descrição em termos da entropia topológica da família das aplicações de Lozi. ### Abstract - In this work, we study the iterations of two dimensional maps. Using symbolic dynamics techniques for two dimensional maps, based on both the kneading theory of Milnor and Thurston and the formalism of symbolic dynamics developed by Sousa Ramos, we studied the qualitative aspects of the dynamics of Lozi maps. Thus, through the symbolic dynamics introduced by Yutaka Ishii, through the correction of symbolic sequence that characterized the first tangency between stable and unstable manifolds, we reformulate the border for the Smale horseshoes. Following this work, we present a method that allows the construction of the basin of attraction for the Lozi attractor. Even using the symbolic dynamics, we introduce a new method, using continuous fractions expansions that allow us to compute the largest Lyapunov exponent. Through the kneading sequence for Lozi map, we characterize the region in the parameter space were we have the kneading curves and we also give a method to the construction of a partition of Markov for the Lozi attractors. Consequently we characterize the topological entropy for the Lozi map, and costruct a new topological invariant, the second invariant.
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Books on the topic "Symbolic dynamics. Topological dynamics"

1

Coornaert, M. Symbolic dynamcis [i.e. dynamics] and hyperbolic groups. Berlin: Springer-Verlag, 1993.

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Kitchens, Bruce P. Symbolic Dynamics. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-642-58822-8.

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Devaney, Robert L., Kit C. Chan, and P. B. Vinod Kumar, eds. Topological Dynamics and Topological Data Analysis. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0174-3.

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de Vries, J. Elements of Topological Dynamics. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-015-8171-4.

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Akin, Ethan. Recurrence in Topological Dynamics. Boston, MA: Springer US, 1997. http://dx.doi.org/10.1007/978-1-4757-2668-8.

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Nerurkar, M. G., D. P. Dokken, and D. B. Ellis, eds. Topological Dynamics and Applications. Providence, Rhode Island: American Mathematical Society, 1998. http://dx.doi.org/10.1090/conm/215.

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Kolyada, Sergiy, Yuri Manin, and Thomas Ward, eds. Algebraic and Topological Dynamics. Providence, Rhode Island: American Mathematical Society, 2005. http://dx.doi.org/10.1090/conm/385.

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Vries, J. de. Elements of topological dynamics. Dordrecht: Kluwer Academic Publishers, 1993.

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J. C. S. P. van der Woude. Topological dynamix. Amsterdam: Centre for Mathematics and Computer Science, 1986.

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Topological dynamix. Amsterdam: Centrum voor Wiskunde en Informatica, 1986.

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Book chapters on the topic "Symbolic dynamics. Topological dynamics"

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Feng, Z., P. Gu, M. Zheng, X. Yan, and D. W. Bao. "Environmental Data-Driven Performance-Based Topological Optimisation for Morphology Evolution of Artificial Taihu Stone." In Proceedings of the 2021 DigitalFUTURES, 117–28. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-5983-6_11.

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AbstractTaihu stone is the most famous one among the top four stones in China. It is formed by the water's erosion in Taihu Lake for hundreds or even thousands of years. It has become a common ornamental stone in classical Chinese gardens because of its porous and intricate forms. At the same time, it has become a cultural symbol through thousands of years of history in China; later, people researched its spatial aesthetics; there are also some studies on its structural properties. For example, it has been found that the opening of Taihu stone caves has a steady-state effect which people develop its value in the theory of Poros City, Porosity in Architecture and some cultural symbols based on the original ornamental value of Taihu stone. This paper introduces a hybrid generative design method that integrates the Computational Fluid Dynamics (CFD) and Bi-directional Evolutionary Structural Optimization (BESO) techniques. Computational Fluid Dynamics (CFD) simulation enables architects and engineers to predict and optimise the performance of buildings and environment in the early stage of the design and topology optimisation techniques BESO has been widely used in structural design to evolve a structure from the full design domain towards an optimum by gradually removing inefficient material and adding materials simultaneously. This research aims to design the artificial Taihu stone based on the environmental data-driven performance feedback using the topological optimisation method. As traditional and historical ornament craftwork in China, the new artificial Taihu stone stimulates thinking about the new value and unique significance of the cultural symbol of Taihu stone in modern society. It proposes possibilities and reflections on exploring the related fields of Porosity in Architecture and Poros City from the perspective of structure.
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Coudène, Yves. "Topological Dynamics." In Universitext, 49–57. London: Springer London, 2016. http://dx.doi.org/10.1007/978-1-4471-7287-1_5.

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Akin, Ethan. "Topological Dynamics." In Mathematics of Complexity and Dynamical Systems, 1726–47. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-1806-1_111.

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Akin, Ethan. "Topological Dynamics." In Encyclopedia of Complexity and Systems Science, 9224–46. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-30440-3_555.

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Barreira, Luís, and Claudia Valls. "Topological Dynamics." In Dynamical Systems by Example, 15–22. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-15915-3_2.

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Barreira, Luís, and Claudia Valls. "Topological Dynamics." In Dynamical Systems by Example, 95–114. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-15915-3_8.

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Glasner, Eli. "Topological dynamics." In Mathematical Surveys and Monographs, 13–47. Providence, Rhode Island: American Mathematical Society, 2003. http://dx.doi.org/10.1090/surv/101/01.

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Barreira, Luis, and Claudia Valls. "Topological Dynamics." In Dynamical Systems, 27–56. London: Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-4835-7_3.

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Kerr, David, and Hanfeng Li. "Topological Dynamics." In Springer Monographs in Mathematics, 163–78. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-49847-8_7.

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Tusset, Gianfranco. "Topological Dynamics." In From Galileo to Modern Economics, 131–48. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95612-1_7.

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Conference papers on the topic "Symbolic dynamics. Topological dynamics"

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Romano, Maria, Paolo Bifulco, Gianni Improta, Giuliana Faiella, Mario Cesarelli, Fabrizio Clemente, and Giovanni D'Addio. "Symbolic dynamics in cardiotocographic monitoring." In 2013 E-Health and Bioengineering Conference (EHB). IEEE, 2013. http://dx.doi.org/10.1109/ehb.2013.6707374.

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Caneco, Acilina, Clara Grácio, and J. Leonel Rocha. "Symbolic dynamics and chaotic synchronization." In Selected Papers from the 3rd Chaotic Modeling and Simulation International Conference (CHAOS2010). WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814350341_0015.

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Luo, C. W., H. J. Chen, H. J. Wang, S. A. Ku, K. H. Wu, T. M. Uen, J. Y. Juang, et al. "Ultrafast dynamics in topological insulators." In SPIE OPTO, edited by Markus Betz, Abdulhakem Y. Elezzabi, Jin-Joo Song, and Kong-Thon Tsen. SPIE, 2013. http://dx.doi.org/10.1117/12.2001954.

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Klaeui, M. "Dynamics of topological spin structures." In 2015 IEEE International Magnetics Conference (INTERMAG). IEEE, 2015. http://dx.doi.org/10.1109/intmag.2015.7157622.

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Wang, Yi, Fangyue Chen, and Yunfang Han. "Glider Dynamics and Topological Dynamics of Bernoulli-shift Rule 61." In 2010 International Workshop on Chaos-Fractals Theories and Applications (IWCFTA). IEEE, 2010. http://dx.doi.org/10.1109/iwcfta.2010.36.

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Sanjith, Bubathi Muruganatham M. A., C. Sujatha, and T. Jayakumar. "Symbolic dynamics based bearing fault detection." In 2012 IEEE 5th India International Conference on Power Electronics (IICPE). IEEE, 2012. http://dx.doi.org/10.1109/iicpe.2012.6450369.

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Wang, Jun, and Jun Wu. "Symbolic Dynamics Analysis of Pathological Signals." In 2011 First International Workshop on Complexity and Data Mining (IWCDM). IEEE, 2011. http://dx.doi.org/10.1109/iwcdm.2011.37.

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Sacramento, P. D. "Dynamics of Quenched Topological Edge Modes." In Symmetry and Structural Properties of Condensed Matter. WORLD SCIENTIFIC, 2017. http://dx.doi.org/10.1142/9789813234345_0006.

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Thacker, Hank. "Topological Charge Membranes and Chiral Dynamics." In The 7th International Workshop on Chiral Dynamics. Trieste, Italy: Sissa Medialab, 2013. http://dx.doi.org/10.22323/1.172.0060.

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Sounas, Dimitrios. "Oscillation dynamics in active topological metamaterials." In Active Photonic Platforms XIII, edited by Ganapathi S. Subramania and Stavroula Foteinopoulou. SPIE, 2021. http://dx.doi.org/10.1117/12.2594971.

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Reports on the topic "Symbolic dynamics. Topological dynamics"

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Burton, Robert M., and Jr. Topics in Stochastics, Symbolic Dynamics and Neural Networks. Fort Belvoir, VA: Defense Technical Information Center, December 1996. http://dx.doi.org/10.21236/ada336426.

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Zurek, Wojciech H., and Adolfo Del Campo. Universality of phase transition dynamics: topological defects from symmetry breaking. Office of Scientific and Technical Information (OSTI), February 2014. http://dx.doi.org/10.2172/1120720.

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Bhatia, Harsh, Attila Gyulassy, Mitchell Ong, Vincenzo Lordi, Erik Draeger, John Pask, Valerio Pascucci, and Peer Timo Bremer. Understanding Lithium Solvation and Diffusion through Topological Analysis of First-Principles Molecular Dynamics. Office of Scientific and Technical Information (OSTI), September 2016. http://dx.doi.org/10.2172/1331475.

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Rechester, A. B., and R. B. White. Chaotic dynamics in plasma: Method of symbolic kinetic equation. Final technical report, September 30, 1991--April 30, 1995. Office of Scientific and Technical Information (OSTI), August 1996. http://dx.doi.org/10.2172/279680.

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