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Dissertations / Theses on the topic 'Ergodic theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 December 2024

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1

Quas, Anthony Nicholas. "Some problems in ergodic theory." Thesis, University of Warwick, 1993. http://wrap.warwick.ac.uk/58569/.

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The thesis consists of a study of problems in ergodic theory relating to one-dimensional dynamical systems, Markov chains and generalizations of Markov chains. It is divided into chapters, three of which have appeared in the literature as papers. Chapter 1 looks at continuous families of circle maps and investigates conditions under which there is a weak*-continuous family of invariant measures. Sufficient conditions are exhibited and the necessity of these conditions is investigated. Chapter 2 is about expanding maps of the interval and the circle, and their relation with g-measures and gener

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2

Bulinski, Kamil. "Interactions between Ergodic Theory and Combinatorial Number Theory." Thesis, The University of Sydney, 2017. http://hdl.handle.net/2123/17733.

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The seminal work of Furstenberg on his ergodic proof of Szemerédi’s Theorem gave rise to a very rich connection between Ergodic Theory and Combinatorial Number Theory (Additive Combinatorics). The former is concerned with dynamics on probability spaces, while the latter is concerned with Ramsey theoretic questions about the integers, as well as other groups. This thesis further develops this symbiosis by establishing various combinatorial results via ergodic techniques, and vice versa. Let us now briefly list some examples of such. A shorter ergodic proof of the following theorem of Magyar is

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3

Butkevich, Sergey G. "Convergence of Averages in Ergodic Theory." The Ohio State University, 2001. http://rave.ohiolink.edu/etdc/view?acc_num=osu980555965.

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4

Butkevich, Sergey. "Convergence of averages in Ergodic Theory /." The Ohio State University, 2000. http://rave.ohiolink.edu/etdc/view?acc_num=osu1488196781735316.

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5

Johnson, Bryan R. "Unconditional convergence of differences in ergodic theory /." The Ohio State University, 1997. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487945015615412.

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6

Jaššová, Alena. "On ergodic theory in non-Archimedean settings." Thesis, University of Liverpool, 2014. http://livrepository.liverpool.ac.uk/2006322/.

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7

Meco, Benjamin. "Ergodic Theory and Applications to Combinatorial Problems." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-409810.

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8

Prabaharan, Kanagarajah. "Topics in ergodic theory : existence of invariant elements and ergodic decompositions of Banach lattices /." The Ohio State University, 1991. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487688973685025.

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9

Cannizzo, Jan. "Schreier Graphs and Ergodic Properties of Boundary Actions." Thesis, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/31444.

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This thesis is broadly concerned with two problems: investigating the ergodic properties of boundary actions, and investigating various properties of Schreier graphs. Our main result concerning the former problem is that, in a variety of situations, the action of an invariant random subgroup of a group G on a boundary of G (e.g. the hyperbolic boundary, or the Poisson boundary) is conservative (there are no wandering sets). This addresses a question asked by Grigorchuk, Kaimanovich, and Nagnibeda and establishes a connection between invariant random subgroups and normal subgroups. We approach

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10

Raissi-Dehkordi, Ramin. "Ergodic theory of dynamical systems having absolutely continuous spectrum." Thesis, University of Cambridge, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.627274.

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11

Li, Kuo-tung. "Convergence problems arising from harmonic analysis and ergodic theory /." The Ohio State University, 1994. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487853913100673.

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12

Snyman, Mathys Machiel. "Ergodic properties of noncommutative dynamical systems." Diss., University of Pretoria, 2013. http://hdl.handle.net/2263/40351.

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In this dissertation we develop aspects of ergodic theory for C*-dynamical systems for which the C*-algebras are allowed to be noncommutative. We define four ergodic properties, with analogues in classic ergodic theory, and study C*-dynamical systems possessing these properties. Our analysis will show that, as in the classical case, only certain combinations of these properties are permissable on C*-dynamical systems. In the second half of this work, we construct concrete noncommutative C*-dynamical systems having various permissable combinations of the ergodic properties. This shows

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13

Beyers, Frederik J. C. "A Hilbert space approach to multiple recurrence in ergodic theory." Pretoria : [s.n.], 2004. http://upetd.up.ac.za/thesis/available/etd-02222006-104936.

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14

Wierdl, Mate. "Almost everywhere convergence and recurrence along subsequences in ergodic theory /." The Ohio State University, 1989. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487672631600881.

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15

Rothlisberger, Matthew Samuel. "Ergodic and Combinatorial Proofs of van der Waerden's Theorem." Scholarship @ Claremont, 2010. http://scholarship.claremont.edu/cmc_theses/14.

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Followed two different proofs of van der Waerden's theorem. Found that the two proofs yield important information about arithmetic progressions and the theorem. van der Waerden's theorem explains the occurrence of arithmetic progressions which can be used to explain such things as the Bible Code.

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16

King, Malcolm Bruce. "Joinings and relative ergodic properties of W*-dynamical systems." Thesis, University of Pretoria, 2019. http://hdl.handle.net/2263/73237.

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We prove a characterization of relative weak mixing in W*-dynamical systems in terms of a relatively independent joining. We then define a noncommutative version of relative discrete spectrum, show that it generalizes both the classical and noncommutative absolute cases and give examples. Chapter 1 reviews the GNS construction for normal states, the related semicyclic representation on von Neumann algebras, Tomita-Takasaki theory and conditional expectations. This will allow us to define, in the tracial case, the basic construction of Vaughan Jones and its associated lifted trace. Dynami

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17

Rehacek, Jan. "Ergodic billiards and mechanism of defocusing in N dimensions." Diss., Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/28886.

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18

Beyers, Frederik Johannes Conradie. "The Szemeredi property in noncommutative dynamical systems." Pretoria : [s.n.], 2009. http://upetd.up.ac.za/thesis/available/etd-05242009-145506.

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19

Kunde, Philipp [Verfasser], and Reiner [Akademischer Betreuer] Lauterbach. "Combinatorial constructions in Smooth Ergodic Theory / Philipp Kunde. Betreuer: Reiner Lauterbach." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2014. http://d-nb.info/1064077056/34.

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20

Munday, Sara Ann. "Finite and infinite ergodic theory for linear and conformal dynamical systems." Thesis, University of St Andrews, 2011. http://hdl.handle.net/10023/3220.

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The first main topic of this thesis is the thorough analysis of two families of piecewise linear maps on the unit interval, the α-Lüroth and α-Farey maps. Here, α denotes a countably infinite partition of the unit interval whose atoms only accumulate at the origin. The basic properties of these maps will be developed, including that each α-Lüroth map (denoted Lα) gives rise to a series expansion of real numbers in [0,1], a certain type of Generalised Lüroth Series. The first example of such an expansion was given by Lüroth. The map Lα is the jump transformation of the corresponding α-Farey

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21

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 multiple

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22

Donoso, Fuentes Sebastián Andrés. "Contributions to ergodic theory and topological dynamics: cube structures and automorphisms." Tesis, Universidad de Chile, 2015. http://repositorio.uchile.cl/handle/2250/135055.

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Doctor en Ciencias de la Ingeniería, Mención Modelación Matemática<br>Esta tesis está consagrada al estudio de diferentes problemas en teoría ergódica y dinámica topológica, relacionados a "estructuras de cubos". Consta de seis capítulos. En la presentación general entregamos resultados generales, ligados en cierta manera a las estructuras de cubos que motivan esta tesis. Comenzamos por las estructuras de cubos introducidas en teoría ergódica por Host y Kra para probar la convergencia en L^2 de medias ergódicas múltiples. Luego presentamos su extensión a dinámica topológica, desarrollada por

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23

Kunde, Philipp Verfasser], and Reiner [Akademischer Betreuer] [Lauterbach. "Combinatorial constructions in Smooth Ergodic Theory / Philipp Kunde. Betreuer: Reiner Lauterbach." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2014. http://d-nb.info/1064077056/34.

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24

Artigiani, Mauro. "Some aspects of diophantine approximation and ergodic theory of translation surfaces." Thesis, University of Bristol, 2016. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.702866.

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This thesis deals with two different topics. In the first part we study Lagrange spectra of Veech translation surfaces, which are a generalisation of the classical Lagrange spectrum. We show that any such Lagrange spectrum contains a Hall ray. We start from the concrete example given by the surface obtained glueing a regular octagon. We use the coding developed by Smillie and Ulcigrai for the surfaces obtained glueing the regular 2ɳ-gons to code geodesics in the Teichmiiller disk of the octagon and prove a formula which allows to express large values in the Lagrange spectrum as sums of Cantor

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25

Mortiss, Genevieve. "Average co-ordinate entropy and a non-singular version of restricted orbit equivalence." [Sydney : University of New South Wales], 1997. http://www.library.unsw.edu.au/~thesis/adt-NUN/public/adt-NUN1998.0001/index.html.

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26

Shi, Ronggang. "Equidistribution of expanding measures with local maximal dimension and Diophantine Approximation." The Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=osu1242259439.

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27

Kaimanovich, Vadim, Klaus Schmidt, and Klaus Schmidt@univie ac at. "Ergodicity of cocycles. 1: General Theory." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi936.ps.

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28

Tanzi, Matteo. "Heterogeneously coupled maps : from high to low dimensional systems through ergodic theory." Thesis, Imperial College London, 2017. http://hdl.handle.net/10044/1/50709.

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In this thesis we study ergodic theoretical properties of high-dimensional systems coupled on graphs. The local dynamics at each node is hyperbolic and coupled with other nodes according to the edges of the graph. We focus our attention on the case of graphs with heterogeneous degrees meaning that most of the nodes make a small number of interactions, while a few hub nodes have very high degree. For such high-dimensional systems there is a regime of the interaction strength for which the coupling is small for poorly connected systems, and large for the hub nodes. In particular, global hyperbol

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29

Griesmer, John Thomas. "Ergodic averages, correlation sequences, and sumsets." Columbus, Ohio : Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view.cgi?acc%5Fnum=osu1243973834.

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30

Jarrett, Kieran. "Non-singular actions of countable groups." Thesis, University of Bath, 2018. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.761021.

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In this thesis we study actions of countable groups on measure spaces underthe assumption that the dynamics are non-singular, with particular reference topointwise ergodic theorems and their relationship to the critical dimensions ofthe action.

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31

Naughton, David Vincent. "On the fine structure of dynamically-defined invariant graphs." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/on-the-fine-structure-of-dynamicallydefined-invariant-graphs(0e81b14b-af68-4433-a983-f98a7b8c5d86).html.

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32

MENDICO, CRISTIAN. "Ergodic behavior of control systems and first-order mean field games." Doctoral thesis, Gran Sasso Science Institute, 2021. http://hdl.handle.net/20.500.12571/23542.

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The work in this thesis concerns the analysis of first-order mean field game (MFG) systems with control of acceleration and the study of the long time-average behavior of control systems of sub-Riemannian type. More precisely, in the first part we begin by studying the well-posedness of the MFG system associated with a control problem with linear state equation. In particular, via a relaxed approach, we prove the existence and the uniqueness of mild solutions and we also study their regularity. Then, we focus on the MFG system with control of the acceleration, a particular case of the one abov

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33

Shereshevsky, Mark Alexandrovich. "On the ergodic theory of cellular automata and two-dimensional Markov shifts generated by them." Thesis, University of Warwick, 1992. http://wrap.warwick.ac.uk/34640/.

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In this thesis we study measurable and topological dynamics of certain classes of cellular automata and multi-dimensional subshifts. In Chapter 1 we consider one-dimensional cellular automata, i.e. the maps T: PZ -> PZ (P is a finite set with more than one element) which are given by (Tx)i==F(xi+1, ..., xi+r), x=(xi)iEZ E PZ for some integers 1≤r and a mapping F: Pr-1+1 -> P. We prove that if F is right- (left-) permutative (in Hedlund's terminology) and 0≤1<r (resp. 1<r≤0), then the natural extension of the dynamical system (PZ,B,μ,T) is a Bernoulli automorphism (μ stands for the (1/p, ..., 1

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34

Mortiss, Genevieve Catherine Mathematics UNSW. "Average co-ordinate entropy and a non-singular version of restricted orbit equivalence." Awarded by:University of New South Wales. Mathematics, 1997. http://handle.unsw.edu.au/1959.4/17823.

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A notion of entropy is defined for the non-singular action of finite co-ordinate changes on X - the infinite product of two- point spaces. This quantity - average co-ordinate or AC entropy - is calculated for product measures and G-measures on X, and an equivalence relation is established for which AC entropy is an invariant. The Inverse Vitali Lemma is discussed in a measure preserving context, and it is shown that for a certain class of measures on X known as odometer bounded, the result will still hold for odometer actions. The foundations for a non-singular version of Rudolph's restricted

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35

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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36

Kadyrov, Shirali. "Entropy and Escape of Mass in Non-Compact Homogeneous Spaces." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1272027404.

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37

Grigo, Alexander. "Billiards and statistical mechanics." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29610.

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Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2009.<br>Committee Chair: Bunimovich, Leonid; Committee Member: Bonetto, Federico; Committee Member: Chow, Shui-Nee; Committee Member: Cvitanovic, Predrag; Committee Member: Weiss, Howard. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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38

Szkola, Arleta. "The Shannon-McMillan theorem and related results for ergodic quantum spin lattice systems and applications in quantum information theory." [S.l.] : [s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=970619588.

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39

Udrea, Bogdan Teodor. "Applications of deformation rigidity theory in Von Neumann algebras." Diss., University of Iowa, 2012. https://ir.uiowa.edu/etd/3395.

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This work contains some structural results for von Neumann algebras arising from measure preserving actions by direct products of groups on probability spaces. The technology and the methods we use are a continuation of those used by Chifan and Sinclair in [10]. By employing these methods, we obtain new examples of strongly solid factors as well as von Neumann algebras with unique or no Cartan subalgebra. We show for instance that every II 1 factor associated with a weakly amenable group in the class S of Ozawa is strongly solid [59]. We also obtain a product version of this result: any maxima

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40

Andrade, Rodrigo Manoel Dias [UNESP]. "Bilhares planares." Universidade Estadual Paulista (UNESP), 2012. http://hdl.handle.net/11449/92952.

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Made available in DSpace on 2014-06-11T19:26:15Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-03-02Bitstream added on 2014-06-13T19:47:09Z : No. of bitstreams: 1 andrade_rmd_me_sjrp.pdf: 453172 bytes, checksum: 949b0dbffc53bf3b227c07bef2ee3856 (MD5)<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)<br>O objetivo principal deste trabalho e estudar a dinâmica de uma partícula pontual no interior de subconjuntos do plano. Tais sistemas são conhecidos na literatura como bilhares. Apresentaremos os principais conceitos desses sistemas e veremos que tais sistemas deix

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41

Karagulyan, Davit. "Certain results on the Möbius disjointness conjecture." Doctoral thesis, KTH, Matematik (Inst.), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-215682.

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We study certain aspects of the Möbius randomness principle and more specifically the Möbius disjointness conjecture of P. Sarnak. In paper A we establish this conjecture for all orientation preserving circle homeomorphisms and continuous interval maps of zero entropy. In paper B we show, that for all subshifts of finite type with positive topological entropy the Möbius disjointness does not hold. In paper C we study a class of three-interval exchange maps arising from a paper of Bourgain and estimate its Hausdorff dimension. In paper D we consider the Chowla and Sarnak conjectures and the Rie

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42

Alves, Fabricio Fernando [UNESP]. "Teorema ergódico multiplicativo de oseledets." Universidade Estadual Paulista (UNESP), 2010. http://hdl.handle.net/11449/94212.

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Made available in DSpace on 2014-06-11T19:26:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-02-18Bitstream added on 2014-06-13T20:16:03Z : No. of bitstreams: 1 alves_ff_me_sjrp.pdf: 362207 bytes, checksum: 9a797ca400dea6e139af98c5a9f10378 (MD5)<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)<br>Este trablaho apresenta os conceitos de Lyapounov e de espaços próprios e fornece um resultado devido a Oseledets, o qual trata da existência desses expoentes (e, consequentemente, dos espaços próprios) do ponto de vista da teoria da medida. A prova do teorema que nós

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43

Samuel, Anthony. "A commutative noncommutative fractal geometry." Thesis, University of St Andrews, 2010. http://hdl.handle.net/10023/1710.

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In this thesis examples of spectral triples, which represent fractal sets, are examined and new insights into their noncommutative geometries are obtained. Firstly, starting with Connes' spectral triple for a non-empty compact totally disconnected subset E of {R} with no isolated points, we develop a noncommutative coarse multifractal formalism. Specifically, we show how multifractal properties of a measure supported on E can be expressed in terms of a spectral triple and the Dixmier trace of certain operators. If E satisfies a given porosity condition, then we prove that the coarse multifract

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44

Bhattad, Kapil. "Joint source channel coding for non-ergodic channels: the distortion signal-to-noise ratio (SNR) exponent perspective." Texas A&M University, 2008. http://hdl.handle.net/1969.1/85928.

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We study the problem of communicating a discrete time analog source over a channel such that the resulting distortion is minimized. For ergodic channels, Shannon showed that separate source and channel coding is optimal. In this work we study this problem for non-ergodic channels. Although not much can be said about the general problem of transmitting any analog sources over any non-ergodic channels with any distortion metric, for many practical problems like video broadcast and voice transmission, we can gain insights by studying the transmission of a Gaussian source over a wireless channel w

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45

Figueiredo, Fernanda Ronssani de. "Medidas que maximizam a entropia no Deslocamento de Haydn." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2015. http://hdl.handle.net/10183/127974.

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Neste trabalho é abordado o exemplo proposto por Nicolai Haydn, no qual é dado um exemplo de um deslocamento onde é possível construir in nitas medidas de máxima entropia, além de in nitos estados de equilíbrio.<br>In this work, we present the example shown by Nicolai Haydn, which is given by subshift where is possible to show in nity measures of maximal entropy, besides in nitely many distinct equilibrium states.

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46

Nasca, Angelo J. III. "The Linear Dynamics of Several Commuting Operators." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1420228736.

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47

Alves, Fabricio Fernando. "Teorema ergódico multiplicativo de oseledets /." São José do Rio Preto : [s.n.], 2010. http://hdl.handle.net/11449/94212.

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Orientador: Vanderlei Minori Horita<br>Banca: Daniel Smania Brandão<br>Banca: Ali Messaoudi<br>Resumo: Este trablaho apresenta os conceitos de Lyapounov e de espaços próprios e fornece um resultado devido a Oseledets, o qual trata da existência desses expoentes (e, consequentemente, dos espaços próprios) do ponto de vista da teoria da medida. A prova do teorema que nós fornecemos foi dada originalmente por Mañe e posteriormente melhorada por Viana.<br>Abstract: This work presents the concepts of Lyapounov exponents and of proper spaces and provides a result due to Oseledets, wich deals with th

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48

Chousionis, Vasileios. "Thermodynamical Formalism." Thesis, University of North Texas, 2004. https://digital.library.unt.edu/ark:/67531/metadc4631/.

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Thermodynamical formalism is a relatively recent area of pure mathematics owing a lot to some classical notions of thermodynamics. On this thesis we state and prove some of the main results in the area of thermodynamical formalism. The first chapter is an introduction to ergodic theory. Some of the main theorems are proved and there is also a quite thorough study of the topology that arises in Borel probability measure spaces. In the second chapter we introduce the notions of topological pressure and measure theoretic entropy and we state and prove two very important theorems, Shannon-McMillan

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49

Gomes, João Tiago Assunção 1986. "Formalismos Gibbsianos para sistemas de spins unidimensionais." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307025.

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Orientador: Eduardo Garibaldi<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>Made available in DSpace on 2018-08-20T22:00:53Z (GMT). No. of bitstreams: 1 Gomes_JoaoTiagoAssuncao_M.pdf: 1424859 bytes, checksum: 6679c0458ae1350513c30bdc7ea2e699 (MD5) Previous issue date: 2012<br>Resumo: Exibir os estados de Gibbs e os estados de equilíbrios para certos sistemas de spins sobre reticulados é um problema de grande interesse para mecânica estatística. Com este intuito, apresentamos para o caso unidimensional dois forma

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50

Mance, Bill. "Normal Numbers with Respect to the Cantor Series Expansion." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1274431587.

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