Ergodic Theory Symbolic Dynamics And Hyperbolic Spaces
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Ergodic Theory Symbolic Dynamics And Hyperbolic Spaces
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Author : T. Bedford
language : en
Publisher: Oxford University Press, USA
Release Date : 1991
Ergodic Theory Symbolic Dynamics And Hyperbolic Spaces written by T. Bedford and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Ergodic theory categories.
Ergodic Theory And Topological Dynamics Of Group Actions On Homogeneous Spaces
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Author : M. Bachir Bekka
language : en
Publisher: Cambridge University Press
Release Date : 2000-05-11
Ergodic Theory And Topological Dynamics Of Group Actions On Homogeneous Spaces written by M. Bachir Bekka and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05-11 with Mathematics categories.
This book, first published in 2000, focuses on developments in the study of geodesic flows on homogenous spaces.
Ergodic Theory Symbolic Dynamics And Hyperbolic Spaces
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Author : Timothy, Bedford
language : en
Publisher:
Release Date : 1991
Ergodic Theory Symbolic Dynamics And Hyperbolic Spaces written by Timothy, Bedford and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Ergodic theory categories.
Symbolic Dynamics
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Author : Bruce P. Kitchens
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-11-14
Symbolic Dynamics written by Bruce P. Kitchens and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-11-14 with Mathematics categories.
Nearly one hundred years ago Jacques Hadamard used infinite sequences of symbols to analyze the distribution of geodesics on certain surfaces. That was the beginning of symbolic dynamics. In the 1930's and 40's Arnold Hedlund and Marston Morse again used infinite sequences to investigate geodesics on surfaces of negative curvature. They coined the term symbolic dynamics and began to study sequence spaces with the shift transformation as dynamical systems. In the 1940's Claude Shannon used sequence spaces to describe infor mation channels. Since that time symbolic dynamics has been used in ergodic theory, topological dynamics, hyperbolic dynamics, information theory and complex dynamics. Symbolic dynamical systems with a finite memory are stud ied in this book. They are the topological Markov shifts. Each can be defined by transition rules and the rules can be summarized by a transition matrix. The study naturally divides into two parts. The first part is about topological Markov shifts where the alphabet is finite. The second part is concerned with topological Markov shifts whose alphabet is count ably infinite. The techniques used in the two cases are quite different. When the alphabet is finite most of the methods are combinatorial or algebraic. When the alphabet is infinite the methods are much more analytic. This book grew from notes for a graduate course taught at Wesleyan Uni versity in the fall of 1994 and is intended as a graduate text and as a reference book for mathematicians working in related fields.
Topological And Ergodic Theory Of Symbolic Dynamics
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Author : Henk Bruin
language : en
Publisher: American Mathematical Society
Release Date : 2023-01-20
Topological And Ergodic Theory Of Symbolic Dynamics written by Henk Bruin and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-20 with Mathematics categories.
Symbolic dynamics is essential in the study of dynamical systems of various types and is connected to many other fields such as stochastic processes, ergodic theory, representation of numbers, information and coding, etc. This graduate text introduces symbolic dynamics from a perspective of topological dynamical systems and presents a vast variety of important examples. After introducing symbolic and topological dynamics, the core of the book consists of discussions of various subshifts of positive entropy, of zero entropy, other non-shift minimal action on the Cantor set, and a study of the ergodic properties of these systems. The author presents recent developments such as spacing shifts, square-free shifts, density shifts, $mathcal{B}$-free shifts, Bratteli-Vershik systems, enumeration scales, amorphic complexity, and a modern and complete treatment of kneading theory. Later, he provides an overview of automata and linguistic complexity (Chomsky's hierarchy). The necessary background for the book varies, but for most of it a solid knowledge of real analysis and linear algebra and first courses in probability and measure theory, metric spaces, number theory, topology, and set theory suffice. Most of the exercises have solutions in the back of the book.
Symbolic Dynamics And Hyperbolic Groups
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Author : Michel Coornaert
language : en
Publisher: Springer
Release Date : 2006-11-14
Symbolic Dynamics And Hyperbolic Groups written by Michel Coornaert and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Gromov's theory of hyperbolic groups have had a big impact in combinatorial group theory and has deep connections with many branches of mathematics suchdifferential geometry, representation theory, ergodic theory and dynamical systems. This book is an elaboration on some ideas of Gromov on hyperbolic spaces and hyperbolic groups in relation with symbolic dynamics. Particular attention is paid to the dynamical system defined by the action of a hyperbolic group on its boundary. The boundary is most oftenchaotic both as a topological space and as a dynamical system, and a description of this boundary and the action is given in terms of subshifts of finite type. The book is self-contained and includes two introductory chapters, one on Gromov's hyperbolic geometry and the other one on symbolic dynamics. It is intended for students and researchers in geometry and in dynamical systems, and can be used asthe basis for a graduate course on these subjects.
Ergodic Theory And Dynamical Systems
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Author : Idris Assani
language : en
Publisher: Walter de Gruyter
Release Date : 2013-12-12
Ergodic Theory And Dynamical Systems written by Idris Assani and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-12 with Mathematics categories.
This is the proceedings of the workshop on recent developments in ergodic theory and dynamical systems on March 2011 and March 2012 at the University of North Carolina at Chapel Hill. The articles in this volume cover several aspects of vibrant research in ergodic theory and dynamical systems. It contains contributions to Teichmuller dynamics, interval exchange transformations, continued fractions, return times averages, Furstenberg Fractals, fractal geometry of non-uniformly hyperbolic horseshoes, convergence along the sequence of squares, adic and horocycle flows, and topological flows. These contributions illustrate the connections between ergodic theory and dynamical systems, number theory, harmonic analysis, probability, and algebra. Two surveys are included which give a nice introduction for interested young or senior researcher to some active research areas. Overall this volume provides a very useful blend of techniques and methods as well as directions of research on general convergence phenomena in ergodic theory and dynamical systems.
An Introduction To Symbolic Dynamics And Coding
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Author : Douglas A. Lind
language : en
Publisher: Cambridge University Press
Release Date : 2021-01-21
An Introduction To Symbolic Dynamics And Coding written by Douglas A. Lind and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-21 with Language Arts & Disciplines categories.
Elementary introduction to symbolic dynamics, updated to describe the main advances in the subject since the original publication in 1995.
Ergodic Theory
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Author : Cesar E. Silva
language : en
Publisher: Springer Nature
Release Date : 2023-07-31
Ergodic Theory written by Cesar E. Silva and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-31 with Mathematics categories.
This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, covers recent developments in classical areas of ergodic theory, including the asymptotic properties of measurable dynamical systems, spectral theory, entropy, ergodic theorems, joinings, isomorphism theory, recurrence, nonsingular systems. It enlightens connections of ergodic theory with symbolic dynamics, topological dynamics, smooth dynamics, combinatorics, number theory, pressure and equilibrium states, fractal geometry, chaos. In addition, the new edition includes dynamical systems of probabilistic origin, ergodic aspects of Sarnak's conjecture, translation flows on translation surfaces, complexity and classification of measurable systems, operator approach to asymptotic properties, interplay with operator algebras
Ergodic Theory Via Joinings
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Author : Eli Glasner
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Ergodic Theory Via Joinings written by Eli Glasner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This textbook focuses on the abstract aspects of topological dynamics and ergodic theory, and presents several examples of the joining technique. The author covers dynamical systems on Lebesgue spaces, the Koopman representation, isometric and weakly mixing extensions, the Furstenberg-Zimmer structure theorem, and the entropy theory for Z-systems. Annotation (c)2003 Book News, Inc., Portland, OR (booknews.com).