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Teses / dissertações sobre o tema "Hyperbolic dynamical systems"

Autor: Grafiati

Publicado: 7 de dezembro de 2024

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1

Ponce, Gabriel. "Fine ergodic properties of partially hyperbolic dynamical systems." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-20032015-113539/.

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Let f : T3 → T3 be a C2 volume preserving partially hyperbolic diffeomorphism homotopic to a linear Anosov automorphism A : T3 → T3. We prove that if f is Kolmogorov, then f is Bernoulli. We study the characteristics of atomic disintegration of the volume measure whenever it occurs. We prove that if the volume measure m has atomic disintegration on the center leaves then the disintegration has one atom per center leaf. We give a condition, depending only on the center Lyapunov exponent of the diffeomorphism, that guarantees atomic disintegration of the volume measure on center leav

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2

Petty, Taylor Michael. "Nonlocally Maximal Hyperbolic Sets for Flows." BYU ScholarsArchive, 2015. https://scholarsarchive.byu.edu/etd/5558.

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In 2004, Fisher constructed a map on a 2-disc that admitted a hyperbolic set not contained in any locally maximal hyperbolic set. Furthermore, it was shown that this was an open property, and that it was embeddable into any smooth manifold of dimension greater than one. In the present work we show that analogous results hold for flows. Specifically, on any smooth manifold with dimension greater than or equal to three there exists an open set of flows such that each flow in the open set contains a hyperbolic set that is not contained in a locally maximal one.

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3

Al-Nayef, Anwar Ali Bayer, and mikewood@deakin edu au. "Semi-hyperbolic mappings in Banach spaces." Deakin University. School of Computing and Mathematics, 1997. http://tux.lib.deakin.edu.au./adt-VDU/public/adt-VDU20051208.110247.

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The definition of semi-hyperbolic dynamical systems generated by Lipschitz continuous and not necessarily invertible mappings in Banach spaces is presented in this thesis. Like hyperbolic mappings, they involve a splitting into stable and unstable spaces, but a slight leakage from the strict invariance of the spaces is possible and the unstable subspaces are assumed to be finite dimensional. Bi-shadowing is a combination of the concepts of shadowing and inverse shadowing and is usually used to compare pseudo-trajectories calculated by a computer with the true trajectories. In this thesis, the

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4

Gaito, Stephen Thomas. "Shadowing of weakly pseudo-hyperbolic pseudo-orbits in discrete dynamical systems." Thesis, University of Warwick, 1992. http://wrap.warwick.ac.uk/109461/.

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We consider Cr (r ≥ 1 +γ) diffeomorphisms of compact Riemannian manifolds. Our aim is to develop the analytic machinery required to describe the topological symbolic dynamics of sets of weakly hyperbolic orbits. The Pesin set is an example of such a set. For Axiom-A dynamical systems, that is, for diffeomorphisms which have a uniformly hyperbolic nonwandering set which is the closure of the periodic orbits, this analytic machinery is provided by the Shadowing Lemma. This lemma is a consequence of the Stable Manifold Theorem, and the local product structure of the nonwandering set of an Axiom-A

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5

Waddington, Simon. "Prime orbit theorems for closed orbits and knots in hyperbolic dynamical systems." Thesis, University of Warwick, 1992. http://wrap.warwick.ac.uk/109425/.

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This thesis consists of four chapters, each with its own notation and references. Chapters 1, 2 and 3 are independent pieces of research. Chapter 0 is an introduction which sets out the definitions and results needed in the main part of the thesis. In Chapter 1, we derive asymptotic formulae for the number of closed orbits of a toral automorphism which is ergodic, but not necessarily hyperbolic. Previously, such formulae were known only in the hyperbolic case. The proof uses an analogy with the Prime Number Theorem. We also give a new proof of the uniform distribution of periodic points. In Ch

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6

Canestrari, Giovanni. "On the Kolmogorov property of a class of infinite measure hyperbolic dynamical systems." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/22352/.

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Smooth maps with singularities describe important physical phenomena such as the collisions of rigid spheres among them and/or with the walls of a container. Questions about the ergodic properties of these models (which can be mapped into billiard models) were first raised by Boltzmann in the nineteenth century and lie at the foundation of Statistical Mechanics. Billiard models also describe the diffusive motion of electrons bouncing off positive nuclei (Lorentz gas models) and in this situation the physical measure can be considered infinite. It is therefore of great importance to study the e

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7

Leclerc, Gaétan. "Nonlinearity, fractals, Fourier decay - harmonic analysis of equilibrium states for hyperbolic dynamical systems." Electronic Thesis or Diss., Sorbonne université, 2024. http://www.theses.fr/2024SORUS264.

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Ce doctorat se situe à l'intersection entre le domaine de la géométrie fractale et des systèmes dynamique hyperbolique. Étant donné un système dynamique hyperbolique dans un espace euclidien (de petite dimension), considérons un sous-ensemble fractal compact invariant, ainsi qu'une mesure de probabilité invariante supportée sur cet ensemble fractal, avec de bonnes propriétés statistiques, telle que la mesure d'entropie maximale. La question est la suivante : la transformée de Fourier de la mesure tends elle vers zéro a la vitesse d'une puissance de xi ? Notre objectif principal est de montrer

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8

Canalias, Vila Elisabet. "Contributions to Libration Orbit Mission Design using Hyperbolic Invariant Manifolds." Doctoral thesis, Universitat Politècnica de Catalunya, 2007. http://hdl.handle.net/10803/5927.

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Aquesta tesi doctoral està emmarcada en el camp de l'astrodinàmica. Presenta solucions a problemes identificats en el disseny de missions que utilitzen òrbites entorn dels punts de libració, fent servir la teoria de sistemes dinàmics.<br/>El problema restringit de tres cossos és un model per estudiar el moviment d'un cos de massa infinitessimal sota l'atracció gravitatòria de dos cossos molt massius. Els cinc punts d'equilibri d'aquest model, en especial L1 i L2, han estat motiu de nombrosos estudis per aplicacions pràctiques en les últimes dècades (SOHO, Genesis...). <br/>Genèricament, qualse

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9

Högele, Michael, and Ilya Pavlyukevich. "Metastability of Morse-Smale dynamical systems perturbed by heavy-tailed Lévy type noise." Universität Potsdam, 2014. http://opus.kobv.de/ubp/volltexte/2014/7063/.

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We consider a general class of finite dimensional deterministic dynamical systems with finitely many local attractors each of which supports a unique ergodic probability measure, which includes in particular the class of Morse–Smale systems in any finite dimension. The dynamical system is perturbed by a multiplicative non-Gaussian heavytailed Lévy type noise of small intensity ε > 0. Specifically we consider perturbations leading to a Itô, Stratonovich and canonical (Marcus) stochastic differential equation. The respective asymptotic first exit time and location problem from each of the domai

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10

Canadell, Cano Marta. "Computation of Normally Hyperbolic Invariant Manifolds." Doctoral thesis, Universitat de Barcelona, 2014. http://hdl.handle.net/10803/277215.

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The subject of the theory of Dynamical Systems is the evolution of systems with respect to time. Hence, it has many applications to other areas of science, such as Physics, Biology, Economics, etc. and it also has interactions with other parts of Mathematics. The global behavior of a dynamical system is organized by its invariant objects, the simplest ones are equilibria and periodic orbits (and related invariant manifolds). Normally hyperbolic invariant manifolds (NHIM for short) are some of these invariant objects. They have the property to persist under small perturbations of the system.

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11

Simmons, Skyler C. "Topological Properties of Invariant Sets for Anosov Maps with Holes." BYU ScholarsArchive, 2011. https://scholarsarchive.byu.edu/etd/3101.

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We begin by studying various topological properties of invariant sets of hyperbolic toral automorphisms in the linear case. Results related to cardinality, local maximality, entropy, and dimension are presented. Where possible, we extend the results to the case of hyperbolic toral automorphisms in higher dimensions, and further to general Anosov maps.

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12

Hemmingsson, Nils. "On the dynamics of a family of critical circle endomorphisms." Thesis, KTH, Matematik (Avd.), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-259743.

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In this thesis we study two seperate yet related three parameter-families of continuously differentiable maps from the unit circle to unit circle which have a single critical point. For one of the families we show that there is a set of positive measure of parameters such that there is a set of positive measure for which all points in the latter set, the derivative experiences exponential growth. We do so by applying a similar methodology to what Michael Benedicks and Lennart Carleson used to study the quadratic family. For the other family we attempt to show a similar but weaker result using

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13

Dutilleul, Tom. "Dynamique chaotique des espaces-temps spatialement homogènes." Thesis, Paris 13, 2019. http://www.theses.fr/2019PA131019.

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En 1963, Belinsky, Khalatnikov et Lifshitz ont proposé une description conjecturale de la géométrie asymptotique des modèles cosmologiques au voisinage de leur singularité initiale. En particulier, il y est avancé que la géométrie asymptotique des espaces-temps spatialement homogènes « génériques » devrait avoir un comportement oscillatoire chaotique modelé sur la dynamique d’une application discrète : l’application de Kasner. Nous démontrons que cette conjecture est vraie au moins pour un ensemble d’espaces-temps de mesure de Lebesgue strictement positive. Dans le contexte des espaces-temps s

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14

Chaves, Daniel Pedro Bezerra. "Sistemas dinâmicos de eventos discretos com aplicação ao fluxo geodésico em superfícies hiperbólicas." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/260471.

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Orientador: Reginaldo Palazzo Júnior<br>Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação<br>Made available in DSpace on 2018-08-19T10:50:06Z (GMT). No. of bitstreams: 1 Chaves_DanielPedroBezerra_D.pdf: 1159929 bytes, checksum: 06894c7e904c6209a690af3080f7cc32 (MD5) Previous issue date: 2011<br>Resumo: Neste trabalho apresentamos um método de descrição combinatorial para o fluxo geodesico sobre uma região hiperbólica compacta, tendo como objetivo associar a seqüências de codificação, parâmetros topologicos oriundos destas superfícies. Isto

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15

Leguil, Martin. "Cocycle dynamics and problems of ergodicity." Thesis, Sorbonne Paris Cité, 2017. http://www.theses.fr/2017USPCC159/document.

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Le travail qui suit comporte quatre chapitres : le premier est centré autour de la propriété de mélange faible pour les échanges d'intervalles et flots de translation. On y présente des résultats obtenus avec Artur Avila qui renforcent des résultats précédents dus à Artur Avila et Giovanni Forni. Le deuxième chapitre est consacré à un travail en commun avec Zhiyuan Zhang et concerne les propriétés d'ergodicité et d'accessibilité stables pour des systèmes partiellement hyperboliques de dimension centrale au moins égale à deux. On montre que sous des hypothèses de cohérence dynamique, center bun

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16

Svanström, Fredrik. "Properties of a generalized Arnold’s discrete cat map." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-35209.

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After reviewing some properties of the two dimensional hyperbolic toral automorphism called Arnold's discrete cat map, including its generalizations with matrices having positive unit determinant, this thesis contains a definition of a novel cat map where the elements of the matrix are found in the sequence of Pell numbers. This mapping is therefore denoted as Pell's cat map. The main result of this thesis is a theorem determining the upper bound for the minimal period of Pell's cat map. From numerical results four conjectures regarding properties of Pell's cat map are also stated. A brief exp

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17

DISCENDENTI, MARCO. "Secondary elliptic islands in a dynamical system close to hyperbolic." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2010. http://hdl.handle.net/2108/1402.

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Consideriamo una famiglia a un parametro di diffeomorfismi simplettici del toro bidimensionale con un punto fisso che passa dall'iperbolicità all'ellitticità. Dimostriamo che esiste un insieme di valori per il parametro per cui la mappa deve avere delle isole ellittiche secondarie.<br>We consider a one parameter family of symplectic maps that cross a non-uniformly hyperbolic situation into an elliptic one. We prove that there exists a set of values of the parameter such that the map has secondary elliptic islands.

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18

Glaister, P. "Approximate Riemann solvers for systems of hyperbolic conservation laws." Thesis, University of Reading, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382211.

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19

Fall, Djiby. "Longtime dynamics of hyperbolic evolutionary equations in ubounded domains and lattice systems." [Tampa, Fla.] : University of South Florida, 2005. http://purl.fcla.edu/fcla/etd/SFE0001053.

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20

Monclair, Daniel. "Dynamique lorentzienne et groupes de difféomorphismes du cercle." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2014. http://tel.archives-ouvertes.fr/tel-01061010.

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Cette thèse comporte deux parties, axées sur des aspects différents de la géométrie lorentzienne. La première partie porte sur les groupes d'isométries de surfaces lorentziennes globalement hyperboliques spatialement compactes, particulièrement lorsque le groupe exhibe une dynamique non triviale (action non propre). Le groupe d'isométries agit naturellement sur le cercle par difféomorphismes, et les résultats principaux portent sur la classification de ces représentations. Sous une hypothèse sur le bord conforme, on obtient une conjugaison par homéomorphisme avec l'action projective d'un sous-

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21

Barril, Basil Carles. "Semilinear hyperbolic equations and the dynamics of gut bacteria." Doctoral thesis, Universitat Autònoma de Barcelona, 2018. http://hdl.handle.net/10803/643304.

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En aquesta tesi proposem un marc matemàtic amb el qual analitzar la dinàmica dels microorganismes que creixen als intestins dels animals. Aquest marc consisteix en un sistema d’EDPs hiperbòliques amb termes de reacció no lineals i certes condicions de frontera que relacionen els microbis de l’ambient amb els que es troben dins els hostes. Al capítol 1 solucionem el Problema Abstracte de Cauchy associat al model considerant la seva formulació semilineal en un determinat espai de Banach X. L’estructura semilineal del sistema obtingut és especial perquè, d’una banda, la llei d’evolució es pot ex

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22

Unterweger, Kristof Gregor [Verfasser]. "High-Performance Coupling of Dynamically Adaptive Grids and Hyperbolic Equation Systems / Kristof Gregor Unterweger." München : Verlag Dr. Hut, 2017. http://d-nb.info/1126296031/34.

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23

Purdy, Daniel S. "An application of the hyperbolic navigation radio system for automated position and control." Thesis, Virginia Tech, 1989. http://hdl.handle.net/10919/46061.

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<p>As automation in the construction site of the future becomes a reality, position location systems are necessary to provide real-time data to an operator. This thesis addresses problems associated with development of a real time automated position location system using a method similar to hyperbolic navigation methods. The Automated Position and Control (APAC) project is a joint effort between the Civil and Electrical Engineering departments at Virginia Polytechnic and State University and Bechtel Eastern Power Corporation.</p><br>Master of Science

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24

Schnellmann, Daniel. "Viana maps and limit distributions of sums of point measures." Phd thesis, KTH, Matematik (Inst.), 2009. http://tel.archives-ouvertes.fr/tel-00694201.

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This thesis consists of five articles mainly devoted to problems in dynamical systems and ergodic theory. We consider non-uniformly hyperbolic two dimensional systems and limit distributions of point measures which are absolutely continuous with respect to the Lebesgue measure. Let $f_{a_0}(x)=a_0-x^2$ be a quadratic map where the parameter $a_0\in(1,2)$ is chosen such that the critical point $0$ is pre-periodic (but not periodic). In Papers A and B we study skew-products $(\th,x)\mapsto F(\th,x)=(g(\th),f_{a_0}(x)+\al s(\th))$, $(\th,x)\in S^1\times\real$. The functions $g:S^1\to S^1$ and $s:

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25

Gersbacher, Christoph [Verfasser], and Dietmar [Akademischer Betreuer] Kröner. "Higher-order discontinuous finite element methods and dynamic model adaptation for hyperbolic systems of conservation laws." Freiburg : Universität, 2017. http://d-nb.info/1136263853/34.

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26

Lichtner, Mark. "Exponential dichotomy and smooth invariant center manifolds for semilinear hyperbolic systems." Doctoral thesis, [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=981306659.

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27

Dalal, Abdulsalam Elmabruk Daw. "Shadow Wave Solutions for Some Balance Law Systems." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2017. https://www.cris.uns.ac.rs/record.jsf?recordId=104976&source=NDLTD&language=en.

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In the first part, the pressureless gas dynamic system with source (body force) is examined and solved by using Shadow Waves. The source represents gravity and Shadow Wave solution (containing the delta function) shows acceleration (contrary to shocks, for example). In the second part, one will nd numerical calculations that conrms the above results.<br>Rad je posvecen analizi modela gasa bez pritiska uz dodatak izvora. Model je resen koriscenjem senka talasa. U ovom slucaju, izvor predstavlja uticaj gravitacije na cestice u modelu. Za razliku od udarnih talasa, talasi senke koje sadrze delta

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28

Sroczinski, Matthias [Verfasser]. "Global existence and asymptotic decay for quasilinear second-order symmetric hyperbolic systems of partial differential equations occurring in the relativistic dynamics of dissipative fluids / Matthias Sroczinski." Konstanz : KOPS Universität Konstanz, 2019. http://d-nb.info/1184795460/34.

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29

Mohammadian, Saeed. "Freeway traffic flow dynamics and safety: A behavioural continuum framework." Thesis, Queensland University of Technology, 2021. https://eprints.qut.edu.au/227209/1/Saeed_Mohammadian_Thesis.pdf.

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Congestion and rear-end crashes are two undesirable phenomena of freeway traffic flows, which are interrelated and highly affected by human psychological factors. Since congestion is an everyday problem, and crashes are rare events, congestion management and crash risk prevention strategies are often implemented through separate research directions. However, overwhelming evidence has underscored the inter-relation between rear-end crashes and freeway traffic flow dynamics in recent decades. This dissertation develops novel mathematical models for freeway traffic flow dynamics and safety to int

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30

Trinh, Ngoc Tu. "Étude sur le contrôle / régulation automatique des systèmes non-linéaires hyperboliques." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSE1195/document.

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Dans cette étude on s'intéresse à la dynamique d'une classe de systèmes non-linéaires décrits par des équations aux dérivées partielles (EDP) du type hyperbolique. L'objectif de l'étude est de construire des lois de contrôle par feedback dynamique de la sortie afin de stabiliser le système autour d'un point d'équilibre d'une part, et, d'autre part, de réguler la sortie vers le point de consigne. Nous considérons la classe des systèmes gouvernés par des EDP quasi-linéaires du type hyperbolique à deux variables indépendantes (une variable temporelle et une variable spatiale). Pour le bien-posé d

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31

Mercier, Magali. "Étude de différents aspects des EDP hyperboliques : persistance d’onde de choc dans la dynamique des fluides compressibles, modélisation du trafic routier, stabilité des lois de conservation scalaires." Thesis, Lyon 1, 2009. http://www.theses.fr/2009LYO10246/document.

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On étudie dans ce travail des systèmes de lois de conservation hyperboliques. La première partie étudie le temps d'existence des solutions régulières et régulières par morceaux de la dynamique des fluides compressibles. Après avoir présenté l'état de l'art en matière de solutions régulières, on montre une extension d'un théorème de Grassin à des gaz de Van der Waals. On étudie ensuite les solutions ondes de chocs : on poursuit l'approche de T. T. Li pour estimer leur temps d'existence dans le cas isentropique à symétrie sphérique, et l'approche de Whitham afin d'obtenir une équation approchée

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32

Al, Zohbi Maryam. "Contributions to the existence, uniqueness, and contraction of the solutions to some evolutionary partial differential equations." Thesis, Compiègne, 2021. http://www.theses.fr/2021COMP2646.

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Dans cette thèse, nous nous sommes principalement intéressés à l’étude théorique et numérique de quelques équations qui décrivent la dynamique des densités des dislocations. Les dislocations sont des défauts microscopiques qui se déplacent dans les matériaux sous l’effet des contraintes extérieures. Dans un premier travail, nous démontrons un résultat d’existence globale en temps des solutions discontinues pour un système hyperbolique diagonal qui n’est pas nécessairement strictement hyperbolique, dans un espace unidimensionnel. Ainsi dans un deuxième travail, nous élargissons notre portée en

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33

Mummert, Anna. "Thermodynamic formalism for nonuniformly hyperbolic dynamical systems." 2006. http://etda.libraries.psu.edu/theses/approved/WorldWideIndex/ETD-1432/index.html.

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34

Whittaker, Michael Fredrick. "Poincaré duality and spectral triples for hyperbolic dynamical systems." Thesis, 2010. http://hdl.handle.net/1828/2897.

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We study aspects of noncommutative geometry on hyperbolic dynamical systems known as Smale spaces. In particular, there are two C*-algebras, defined on the stable and unstable groupoids arising from the hyperbolic dynamics. These give rise to two additional crossed product C*-algebras known as the stable and unstable Ruelle algebras. We show that the Ruelle algebras exhibit noncommutative Poincaré duality. As a consequence we obtain isomorphisms between the K-theory and K-homology groups of the stable and unstable Ruelle algebras. A second result defines spectral triples on these C*-algebras a

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35

Carrasco, Correa Pablo Daniel. "Compact Dynamical Foliations." Thesis, 2011. http://hdl.handle.net/1807/27574.

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According to the work of Dennis Sullivan, there exists a smooth flow on the 5-sphere all of whose orbits are periodic although there is no uniform bound on their periods. The question addressed in this thesis is whether such an example can occur in the partially hyperbolic context. That is, does there exist a partially hyperbolic diffeomorphism of a compact manifold such that all the leaves of its center foliation are compact although there is no uniform bound for their volumes. We will show that the answer to the previous question under the very mild hypothesis of dynamical coherence is no

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36

Talitskaya, Anna. "Partially hyperbolic phenomena in dynamical systems with discrete and continuous time." 2004. http://etda.libraries.psu.edu/theses/approved/WorldWideIndex/ETD-533/index.html.

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37

"Some new results on hyperbolic gauss curvature flows." Thesis, 2011. http://library.cuhk.edu.hk/record=b6075160.

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Wo, Weifeng.<br>Thesis (Ph.D.)--Chinese University of Hong Kong, 2011.<br>Includes bibliographical references (leaves 99-102).<br>Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.<br>Abstract also in Chinese.

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38

Wieler, Susana. "Smale spaces with totally disconnected local stable sets." Thesis, 2012. http://hdl.handle.net/1828/3905.

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A Smale space is a chaotic dynamical system with canonical coordinates of contracting and expanding directions. The basic sets for Smale’s Axiom A systems are a key class of examples. R.F. Williams considered the special case where the basic set had a totally disconnected contracting set and a Euclidean expanding one. He provided a construction using inverse limits of such examples and also proved that (under appropriate hyptotheses) all such basic sets arose from this construction. We will be working in the metric setting of Smale spaces, but the goal is to extend Williams’ results by removin

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39

Bohnet, Doris. "Partially hyperbolic diffeomorphisms with a compact center foliation with finite holonomy." Phd thesis, 2011. http://tel.archives-ouvertes.fr/tel-00782664.

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On démontre que les difféomorphismes partiellement hyperboliques admettant un feuilletage central invariant compact sont dynamiquement cohérent et en plus ils ont la propriété de pistage. En supposant une direction instable uni-dimensionnelle et orientée on peut prouver que le difféomorphisme projette en un automorphisme hyperbolique de tore dans l'espace des feuilles centrales.

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Wieler, Susana. "Symbolic and geometric representations of unimodular Pisot substitutions." Thesis, 2007. http://hdl.handle.net/1828/131.

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We review the construction of three Smale spaces associated to a unimodular Pisot substitution on d letters: a subshift of finite type (SFT), a substitution tiling space, and a hyperbolic toral automorphism on the Euclidean d-torus. By considering an SFT whose elements are biinfinite, rather than infinite, paths in the graph associated to the substitution, we modify a well-known map to obtain a factor map between our SFT and the hyperbolic toral automorphism on the d-torus given by the incidence matrix of the substitution. We prove that if the tiling substitution forces its border, then this

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Garg, Naveen Kumar. "Novel Upwind and Central Schemes for Various Hyperbolic Systems." Thesis, 2017. http://etd.iisc.ac.in/handle/2005/3564.

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The class of hyperbolic conservation laws model the phenomena of non-linear wave propagation, including the presence and propagation of discontinuities and expansion waves. Such nonlinear systems can generate discontinuities in the so-lution even for smooth initial conditions. Presence of discontinuities results in break down of a solution in the classical sense and to show existence, weak for-mulation of a problem is required. Moreover, closed form solutions are di cult to obtain and in some cases such solutions are even unavailable. Thus, numerical algorithms play an important role in solvin

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42

Garg, Naveen Kumar. "Novel Upwind and Central Schemes for Various Hyperbolic Systems." Thesis, 2017. http://etd.iisc.ernet.in/2005/3564.

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The class of hyperbolic conservation laws model the phenomena of non-linear wave propagation, including the presence and propagation of discontinuities and expansion waves. Such nonlinear systems can generate discontinuities in the so-lution even for smooth initial conditions. Presence of discontinuities results in break down of a solution in the classical sense and to show existence, weak for-mulation of a problem is required. Moreover, closed form solutions are di cult to obtain and in some cases such solutions are even unavailable. Thus, numerical algorithms play an important role in solvin

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43

Kaushik, K. N. "A Low Dissipative Relaxation Scheme For Hyperbolic Consevation Laws." Thesis, 2005. https://etd.iisc.ac.in/handle/2005/1661.

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Kaushik, K. N. "A Low Dissipative Relaxation Scheme For Hyperbolic Consevation Laws." Thesis, 2005. http://etd.iisc.ernet.in/handle/2005/1661.

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Hante, Falk Michael [Verfasser]. "Hybrid dynamics comprising modes governed by partial differential equations : modeling, analysis and control for semilinear hyperbolic systems in one space dimension / vorgelgt von Falk Michael Hante." 2010. http://d-nb.info/1006656782/34.

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El-Khatib, Mayar. "Highway Development Decision-Making Under Uncertainty: Analysis, Critique and Advancement." Thesis, 2010. http://hdl.handle.net/10012/5741.

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While decision-making under uncertainty is a major universal problem, its implications in the field of transportation systems are especially enormous; where the benefits of right decisions are tremendous, the consequences of wrong ones are potentially disastrous. In the realm of highway systems, decisions related to the highway configuration (number of lanes, right of way, etc.) need to incorporate both the traffic demand and land price uncertainties. In the literature, these uncertainties have generally been modeled using the Geometric Brownian Motion (GBM) process, which has been used extens

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