Ergodic Dynamics

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Ergodic Dynamics

Jane Hawkins
Ergodic Dynamics Book PDF

Author : Jane Hawkins
Publisher : Springer Nature
Page : 340 pages
File Size : 45,5 Mb
Release : 2021-01-28
Category : Mathematics
ISBN : 9783030592424

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Ergodic Dynamics by Jane Hawkins Pdf

This textbook provides a broad introduction to the fields of dynamical systems and ergodic theory. Motivated by examples throughout, the author offers readers an approachable entry-point to the dynamics of ergodic systems. Modern and classical applications complement the theory on topics ranging from financial fraud to virus dynamics, offering numerous avenues for further inquiry. Starting with several simple examples of dynamical systems, the book begins by establishing the basics of measurable dynamical systems, attractors, and the ergodic theorems. From here, chapters are modular and can be selected according to interest. Highlights include the Perron–Frobenius theorem, which is presented with proof and applications that include Google PageRank. An in-depth exploration of invariant measures includes ratio sets and type III measurable dynamical systems using the von Neumann factor classification. Topological and measure theoretic entropy are illustrated and compared in detail, with an algorithmic application of entropy used to study the papillomavirus genome. A chapter on complex dynamics introduces Julia sets and proves their ergodicity for certain maps. Cellular automata are explored as a series of case studies in one and two dimensions, including Conway’s Game of Life and latent infections of HIV. Other chapters discuss mixing properties, shift spaces, and toral automorphisms. Ergodic Dynamics unifies topics across ergodic theory, topological dynamics, complex dynamics, and dynamical systems, offering an accessible introduction to the area. Readers across pure and applied mathematics will appreciate the rich illustration of the theory through examples, real-world connections, and vivid color graphics. A solid grounding in measure theory, topology, and complex analysis is assumed; appendices provide a brief review of the essentials from measure theory, functional analysis, and probability.

Smooth Ergodic Theory of Random Dynamical Systems

Pei-Dong Liu,Min Qian
Smooth Ergodic Theory of Random Dynamical Systems Book PDF

Author : Pei-Dong Liu,Min Qian
Publisher : Springer
Page : 233 pages
File Size : 52,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540492917

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Smooth Ergodic Theory of Random Dynamical Systems by Pei-Dong Liu,Min Qian Pdf

This book studies ergodic-theoretic aspects of random dynam- ical systems, i.e. of deterministic systems with noise. It aims to present a systematic treatment of a series of recent results concerning invariant measures, entropy and Lyapunov exponents of such systems, and can be viewed as an update of Kifer's book. An entropy formula of Pesin's type occupies the central part. The introduction of relation numbers (ch.2) is original and most methods involved in the book are canonical in dynamical systems or measure theory. The book is intended for people interested in noise-perturbed dynam- ical systems, and can pave the way to further study of the subject. Reasonable knowledge of differential geometry, measure theory, ergodic theory, dynamical systems and preferably random processes is assumed.

Ergodic Theory and Differentiable Dynamics

Ricardo Mañé
Ergodic Theory and Differentiable Dynamics Book PDF

Author : Ricardo Mañé
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 55,8 Mb
Release : 1987-01
Category : Entropia
ISBN : 3540152784

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Ergodic Theory and Differentiable Dynamics by Ricardo Mañé Pdf

This version differs from the Portuguese edition only in a few additions and many minor corrections. Naturally, this edition raised the question of whether to use the opportunity to introduce major additions. In a book like this, ending in the heart of a rich research field, there are always further topics that should arguably be included. Subjects like geodesic flows or the role of Hausdorff dimension in con­ temporary ergodic theory are two of the most tempting gaps to fill. However, I let it stand with practically the same boundaries as the original version, still believing these adequately fulfill its goal of presenting the basic knowledge required to approach the research area of Differentiable Ergodic Theory. I wish to thank Dr. Levy for the excellent translation and several of the correc­ tions mentioned above. Rio de Janeiro, January 1987 Ricardo Mane Introduction This book is an introduction to ergodic theory, with emphasis on its relationship with the theory of differentiable dynamical systems, which is sometimes called differentiable ergodic theory. Chapter 0, a quick review of measure theory, is included as a reference. Proofs are omitted, except for some results on derivatives with respect to sequences of partitions, which are not generally found in standard texts on measure and integration theory and tend to be lost within a much wider framework in more advanced texts.

Ergodic Theory and Dynamical Systems

Yves Coudène
Ergodic Theory and Dynamical Systems Book PDF

Author : Yves Coudène
Publisher : Springer
Page : 190 pages
File Size : 45,9 Mb
Release : 2016-11-10
Category : Mathematics
ISBN : 9781447172871

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Ergodic Theory and Dynamical Systems by Yves Coudène Pdf

This textbook is a self-contained and easy-to-read introduction to ergodic theory and the theory of dynamical systems, with a particular emphasis on chaotic dynamics. This book contains a broad selection of topics and explores the fundamental ideas of the subject. Starting with basic notions such as ergodicity, mixing, and isomorphisms of dynamical systems, the book then focuses on several chaotic transformations with hyperbolic dynamics, before moving on to topics such as entropy, information theory, ergodic decomposition and measurable partitions. Detailed explanations are accompanied by numerous examples, including interval maps, Bernoulli shifts, toral endomorphisms, geodesic flow on negatively curved manifolds, Morse-Smale systems, rational maps on the Riemann sphere and strange attractors. Ergodic Theory and Dynamical Systems will appeal to graduate students as well as researchers looking for an introduction to the subject. While gentle on the beginning student, the book also contains a number of comments for the more advanced reader.

Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces

M. Bachir Bekka,Matthias Mayer
Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces Book PDF

Author : M. Bachir Bekka,Matthias Mayer
Publisher : Cambridge University Press
Page : 214 pages
File Size : 55,8 Mb
Release : 2000-05-11
Category : Mathematics
ISBN : 0521660300

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Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces by M. Bachir Bekka,Matthias Mayer Pdf

This book, first published in 2000, focuses on developments in the study of geodesic flows on homogenous spaces.

Ergodic Theory

Manfred Einsiedler,Thomas Ward
Ergodic Theory Book PDF

Author : Manfred Einsiedler,Thomas Ward
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 54,9 Mb
Release : 2010-09-11
Category : Mathematics
ISBN : 9780857290212

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Ergodic Theory by Manfred Einsiedler,Thomas Ward Pdf

This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.

Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics

Sébastien Ferenczi,Joanna Kułaga-Przymus,Mariusz Lemańczyk
Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics Book PDF

Author : Sébastien Ferenczi,Joanna Kułaga-Przymus,Mariusz Lemańczyk
Publisher : Springer
Page : 434 pages
File Size : 45,8 Mb
Release : 2018-06-15
Category : Mathematics
ISBN : 9783319749082

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Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics by Sébastien Ferenczi,Joanna Kułaga-Przymus,Mariusz Lemańczyk Pdf

This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Möbius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described.

Dynamical Systems and Ergodic Theory

Mark Pollicott,Michiko Yuri
Dynamical Systems and Ergodic Theory Book PDF

Author : Mark Pollicott,Michiko Yuri
Publisher : Unknown
Page : 128 pages
File Size : 42,7 Mb
Release : 2013-07-13
Category : Electronic
ISBN : 1299733905

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Dynamical Systems and Ergodic Theory by Mark Pollicott,Michiko Yuri Pdf

Essentially a self-contained text giving an introduction to topological dynamics and ergodic theory.

Topics in Dynamics and Ergodic Theory

Sergey Bezuglyi
Topics in Dynamics and Ergodic Theory Book PDF

Author : Sergey Bezuglyi
Publisher : Cambridge University Press
Page : 276 pages
File Size : 45,7 Mb
Release : 2003-12-08
Category : Mathematics
ISBN : 0521533651

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Topics in Dynamics and Ergodic Theory by Sergey Bezuglyi Pdf

This book contains a collection of survey papers by leading researchers in ergodic theory, low-dimensional and topological dynamics and it comprises nine chapters on a range of important topics. These include: the role and usefulness of ultrafilters in ergodic theory, topological dynamics and Ramsey theory; topological aspects of kneading theory together with an analogous 2-dimensional theory called pruning; the dynamics of Markov odometers, Bratteli-Vershik diagrams and orbit equivalence of non-singular automorphisms; geometric proofs of Mather's connecting and accelerating theorems; recent results in one dimensional smooth dynamics; periodic points of nonexpansive maps; arithmetic dynamics; the defect of factor maps; entropy theory for actions of countable amenable groups.

Ergodic Theory and Topological Dynamics

Anonim
Ergodic Theory and Topological Dynamics Book PDF

Author : Anonim
Publisher : Academic Press
Page : 189 pages
File Size : 42,8 Mb
Release : 1976-11-15
Category : Mathematics
ISBN : 0080873863

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Ergodic Theory and Topological Dynamics by Anonim Pdf

Ergodic Theory and Topological Dynamics

Dynamics, Ergodic Theory and Geometry

Boris Hasselblatt
Dynamics Ergodic Theory and Geometry Book PDF

Author : Boris Hasselblatt
Publisher : Cambridge University Press
Page : 324 pages
File Size : 47,5 Mb
Release : 2007-09-24
Category : Mathematics
ISBN : 9780521875417

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Dynamics, Ergodic Theory and Geometry by Boris Hasselblatt Pdf

Based on the subjects from the Clay Mathematics Institute/Mathematical Sciences Research Institute Workshop titled 'Recent Progress in Dynamics' in September and October 2004, this volume contains surveys and research articles by leading experts in several areas of dynamical systems that have experienced substantial progress. One of the major surveys is on symplectic geometry, which is closely related to classical mechanics and an exciting addition to modern geometry. The survey on local rigidity of group actions gives a broad and up-to-date account of another flourishing subject. Other papers cover hyperbolic, parabolic, and symbolic dynamics as well as ergodic theory. Students and researchers in dynamical systems, geometry, and related areas will find this book fascinating. The book also includes a fifty-page commented problem list that takes the reader beyond the areas covered by the surveys, to inspire and guide further research.

Topological and Ergodic Theory of Symbolic Dynamics

Henk Bruin
Topological and Ergodic Theory of Symbolic Dynamics Book PDF

Author : Henk Bruin
Publisher : American Mathematical Society
Page : 481 pages
File Size : 49,9 Mb
Release : 2023-01-20
Category : Mathematics
ISBN : 9781470469849

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Topological and Ergodic Theory of Symbolic Dynamics by Henk Bruin Pdf

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.

Ergodic Theory, Hyperbolic Dynamics and Dimension Theory

Luís Barreira
Ergodic Theory Hyperbolic Dynamics and Dimension Theory Book PDF

Author : Luís Barreira
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 54,7 Mb
Release : 2012-04-28
Category : Mathematics
ISBN : 9783642280900

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Ergodic Theory, Hyperbolic Dynamics and Dimension Theory by Luís Barreira Pdf

Over the last two decades, the dimension theory of dynamical systems has progressively developed into an independent and extremely active field of research. The main aim of this volume is to offer a unified, self-contained introduction to the interplay of these three main areas of research: ergodic theory, hyperbolic dynamics, and dimension theory. It starts with the basic notions of the first two topics and ends with a sufficiently high-level introduction to the third. Furthermore, it includes an introduction to the thermodynamic formalism, which is an important tool in dimension theory. The volume is primarily intended for graduate students interested in dynamical systems, as well as researchers in other areas who wish to learn about ergodic theory, thermodynamic formalism, or dimension theory of hyperbolic dynamics at an intermediate level in a sufficiently detailed manner. In particular, it can be used as a basis for graduate courses on any of these three subjects. The text can also be used for self-study: it is self-contained, and with the exception of some well-known basic facts from other areas, all statements include detailed proofs.

Ergodic Theory, Open Dynamics, and Coherent Structures

Wael Bahsoun,Christopher Bose,Gary Froyland
Ergodic Theory Open Dynamics and Coherent Structures Book PDF

Author : Wael Bahsoun,Christopher Bose,Gary Froyland
Publisher : Springer
Page : 0 pages
File Size : 54,7 Mb
Release : 2016-08-23
Category : Mathematics
ISBN : 149394326X

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Ergodic Theory, Open Dynamics, and Coherent Structures by Wael Bahsoun,Christopher Bose,Gary Froyland Pdf

This book is comprised of selected research articles developed from a workshop on Ergodic Theory, Probabilistic Methods and Applications, held in April 2012 at the Banff International Research Station. It contains contributions from world leading experts in ergodic theory, numerical dynamical systems, molecular dynamics and ocean/atmosphere dynamics, nonequilibrium statistical mechanics. The volume will serve as a valuable reference for mathematicians, physicists, engineers, biologists and climate scientists, who currently use, or wish to learn how to use, probabilistic techniques to cope with dynamical models that display open or non-equilibrium behavior.

Combinatorial Constructions in Ergodic Theory and Dynamics

A. B. Katok
Combinatorial Constructions in Ergodic Theory and Dynamics Book PDF

Author : A. B. Katok
Publisher : American Mathematical Soc.
Page : 127 pages
File Size : 44,8 Mb
Release : 2003
Category : Combinatorial analysis
ISBN : 9780821834961

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Combinatorial Constructions in Ergodic Theory and Dynamics by A. B. Katok Pdf

Ergodic theory studies measure-preserving transformations of measure spaces. These objects are intrinsically infinite, and the notion of an individual point or of an orbit makes no sense. Still there are a variety of situations when a measure preserving transformation (and its asymptotic behavior) can be well described as a limit of certain finite objects (periodic processes). The first part of this book develops this idea systematically. Genericity of approximation in various categories is explored, and numerous applications are presented, including spectral multiplicity and properties of the maximal spectral type. The second part of the book contains a treatment of various constructions of cohomological nature with an emphasis on obtaining interesting asymptotic behavior from approximate pictures at different time scales. The book presents a view of ergodic theory not found in other expository sources. It is suitable for graduate students familiar with measure theory and basic functional analysis.