Automorphisms And Equivalence Relations In Topological Dynamics
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Automorphisms And Equivalence Relations In Topological Dynamics
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Author : David Ellis
language : en
Publisher:
Release Date : 2014
Automorphisms And Equivalence Relations In Topological Dynamics written by David Ellis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Algebraic topology categories.
A lucid and self-contained treatment of many key ideas in topological dynamics, achieved by focusing on equivalence relations and automorphisms.
Automorphisms And Equivalence Relations In Topological Dynamics
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Author : David B. Ellis
language : en
Publisher: Cambridge University Press
Release Date : 2014-06-05
Automorphisms And Equivalence Relations In Topological Dynamics written by David B. Ellis 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 2014-06-05 with Mathematics categories.
A lucid and self-contained treatment of many key ideas in topological dynamics, achieved by focusing on equivalence relations and automorphisms.
Topological Entropy And Equivalence Of Dynamical Systems
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Author : Roy L. Adler
language : en
Publisher: American Mathematical Soc.
Release Date : 1979
Topological Entropy And Equivalence Of Dynamical Systems written by Roy L. Adler 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 1979 with Ergodic theory categories.
The purpose of this work is to prove a theorem for topological entropy analogous to Ornstein's result for measure entropy. For this a natural class of dynamical systems is needed to play the same role for topological entropy as the Bernoulli shifts do for measure entropy. Fortunately there is just such a class--the topological Markov shifts. The main result of this paper is that topological entropy along with another number, called the ergodic period, is a complete set of invariants under this new equivalence relation for the class of topological Markov shifts.
C Algebras Of Homoclinic And Heteroclinic Structure In Expansive Dynamics
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Author : Klaus Thomsen
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-06-11
C Algebras Of Homoclinic And Heteroclinic Structure In Expansive Dynamics written by Klaus Thomsen 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 2010-06-11 with Mathematics categories.
The author unifies various constructions of $C^*$-algebras from dynamical systems, specifically, the dimension group construction of Krieger for shift spaces, the corresponding constructions of Wagoner and Boyle, Fiebig and Fiebig for countable state Markov shifts and one-sided shift spaces, respectively, and the constructions of Ruelle and Putnam for Smale spaces. The general setup is used to analyze the structure of the $C^*$-algebras arising from the homoclinic and heteroclinic equivalence relations in expansive dynamical systems, in particular, expansive group endomorphisms and automorphisms and generalized 1-solenoids. For these dynamical systems it is shown that the $C^*$-algebras are inductive limits of homogeneous or sub-homogeneous algebras with one-dimensional spectra.
Textile Systems For Endomorphisms And Automorphisms Of The Shift
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Author : Masakazu Nasu
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Textile Systems For Endomorphisms And Automorphisms Of The Shift written by Masakazu Nasu 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 1995 with Mathematics categories.
We introduce the notion of a textile system. Using this, we study the dynamical properties of endomorphisms and automorphisms of topological Markov shifts including one-sided ones. The dynamical properties of automorphisms of sofic systems are also studied.
Topological Dynamics Of Enveloping Semigroups
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Author : Anima Nagar
language : en
Publisher: Springer Nature
Release Date : 2023-01-01
Topological Dynamics Of Enveloping Semigroups written by Anima Nagar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Mathematics categories.
This book introduces the theory of enveloping semigroups—an important tool in the field of topological dynamics—introduced by Robert Ellis. The book deals with the basic theory of topological dynamics and touches on the advanced concepts of the dynamics of induced systems and their enveloping semigroups. All the chapters in the book are well organized and systematically dealing with introductory topics through advanced research topics. The basic concepts give the motivation to begin with, then the theory, and finally the new research-oriented topics. The results are presented with detailed proof, plenty of examples and several open questions are put forward to motivate for future research. Some of the results, related to the enveloping semigroup, are new to the existing literature. The enveloping semigroups of the induced systems is considered for the first time in the literature, and some new results are obtained. The book has a research-oriented flavour in the field of topological dynamics.
Global Aspects Of Ergodic Group Actions
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Author : A. S. Kechris
language : en
Publisher:
Release Date : 2014-05-21
Global Aspects Of Ergodic Group Actions written by A. S. Kechris and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-21 with MATHEMATICS categories.
"The subject of this book is the study of ergodic, measure preserving actions of countable discrete groups on standard probability spaces. It explores a direction that emphasizes a global point of view, concentrating on the structure of the space of measure preserving actions of a given group and its associated cocycle spaces. These are equipped with canonical topological actions that give rise to the usual concepts of conjugacy of actions and cohomology of cocycles. Structural properties of discrete groups such as amenability, Kazhdan's property (T) and the Haagerup Approximation Property play a significant role in this theory as they have important connections to the global structure of these spaces. One of the main topics discussed in this book is the analysis of the complexity of the classification problems of conjugacy and orbit equivalence of actions, as well as of cohomology of cocycles. This involves ideas from topological dynamics, descriptive set theory, harmonic analysis, and the theory of unitary group representations. Also included is a study of properties of the automorphism group of a standard probability space and some of its important subgroups, such as the full and automorphism groups of measure preserving equivalence relations and connections with the theory of costs. The book contains nine appendices that present necessary background material in functional analysis, measure theory, and group representations, thus making the book accessible to a wider audience."--Publisher's website.
Elements Of Dynamical Systems
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Author : Anima Nagar
language : en
Publisher: Springer Nature
Release Date : 2022-11-11
Elements Of Dynamical Systems written by Anima Nagar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-11 with Mathematics categories.
This book stems from lectures that were delivered at the three-week Advanced Instructional School on Ergodic Theory and Dynamical Systems held at the Indian Institute of Technology Delhi, from 4–23 December 2017, with the support of the National Centre for Mathematics, National Board for Higher Mathematics, Department of Atomic Energy, Government of India. The book discusses various aspects of dynamical systems. Each chapter of this book specializes in one aspect of dynamical systems and thus begins at an elementary level and goes on to cover fairly advanced material. The book helps researchers be familiar with and navigate through different parts of ergodic theory and dynamical systems.
Crossed Products Of C Algebras Topological Dynamics And Classification
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Author : Thierry Giordano
language : en
Publisher: Springer
Release Date : 2018-08-28
Crossed Products Of C Algebras Topological Dynamics And Classification written by Thierry Giordano and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-28 with Mathematics categories.
This book collects the notes of the lectures given at an Advanced Course on Dynamical Systems at the Centre de Recerca Matemàtica (CRM) in Barcelona. The notes consist of four series of lectures. The first one, given by Andrew Toms, presents the basic properties of the Cuntz semigroup and its role in the classification program of simple, nuclear, separable C*-algebras. The second series of lectures, delivered by N. Christopher Phillips, serves as an introduction to group actions on C*-algebras and their crossed products, with emphasis on the simple case and when the crossed products are classifiable. The third one, given by David Kerr, treats various developments related to measure-theoretic and topological aspects of crossed products, focusing on internal and external approximation concepts, both for groups and C*-algebras. Finally, the last series of lectures, delivered by Thierry Giordano, is devoted to the theory of topological orbit equivalence, with particular attention to the classification of minimal actions by finitely generated abelian groups on the Cantor set.
Global Aspects Of Ergodic Group Actions
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Author : A. S. Kechris
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-01-01
Global Aspects Of Ergodic Group Actions written by A. S. Kechris 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 2010-01-01 with Mathematics categories.
"The subject of this book is the study of ergodic, measure preserving actions of countable discrete groups on standard probability spaces. It explores a direction that emphasizes a global point of view, concentrating on the structure of the space of measure preserving actions of a given group and its associated cocycle spaces. These are equipped with canonical topological actions that give rise to the usual concepts of conjugacy of actions and cohomology of cocycles. Structural properties of discrete groups such as amenability, Kazhdan's property (T) and the Haagerup Approximation Property play a significant role in this theory as they have important connections to the global structure of these spaces. One of the main topics discussed in this book is the analysis of the complexity of the classification problems of conjugacy and orbit equivalence of actions, as well as of cohomology of cocycles. This involves ideas from topological dynamics, descriptive set theory, harmonic analysis, and the theory of unitary group representations. Also included is a study of properties of the automorphism group of a standard probability space and some of its important subgroups, such as the full and automorphism groups of measure preserving equivalence relations and connections with the theory of costs. The book contains nine appendices that present necessary background material in functional analysis, measure theory, and group representations, thus making the book accessible to a wider audience."--Publisher's website.