Ergodic Dynamics
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Ergodic Dynamics
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Author : Jane Hawkins
language : en
Publisher: Springer Nature
Release Date : 2021-01-28
Ergodic Dynamics written by Jane Hawkins and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-28 with Mathematics categories.
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.
Ergodic Theory And Dynamical Systems
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Author : Yves Coudène
language : en
Publisher: Springer
Release Date : 2016-11-10
Ergodic Theory And Dynamical Systems written by Yves Coudène and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-10 with Mathematics categories.
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
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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.
Combinatorial Constructions In Ergodic Theory And Dynamics
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Author : A. B. Katok
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Combinatorial Constructions In Ergodic Theory And Dynamics written by A. B. Katok 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.
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.
Ergodic Theory
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Author : Manfred Einsiedler
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-11
Ergodic Theory written by Manfred Einsiedler 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 2010-09-11 with Mathematics categories.
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 Hyperbolic Dynamics And Dimension Theory
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Author : Luís Barreira
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-28
Ergodic Theory Hyperbolic Dynamics And Dimension Theory written by Luís Barreira 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 2012-04-28 with Mathematics categories.
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.
Dynamical Systems And Ergodic Theory
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Author : Mark Pollicott
language : en
Publisher:
Release Date : 2013-07-13
Dynamical Systems And Ergodic Theory written by Mark Pollicott and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-13 with categories.
Essentially a self-contained text giving an introduction to topological dynamics and ergodic theory.
Ergodic Theory Of Random Transformations
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Author : Yuri Kifer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Ergodic Theory Of Random Transformations written by Yuri Kifer 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 2012-12-06 with Mathematics categories.
Ergodic theory of dynamical systems i.e., the qualitative analysis of iterations of a single transformation is nowadays a well developed theory. In 1945 S. Ulam and J. von Neumann in their short note [44] suggested to study ergodic theorems for the more general situation when one applies in turn different transforma tions chosen at random. Their program was fulfilled by S. Kakutani [23] in 1951. 'Both papers considered the case of transformations with a common invariant measure. Recently Ohno [38] noticed that this condition was excessive. Ergodic theorems are just the beginning of ergodic theory. Among further major developments are the notions of entropy and characteristic exponents. The purpose of this book is the study of the variety of ergodic theoretical properties of evolution processes generated by independent applications of transformations chosen at random from a certain class according to some probability distribution. The book exhibits the first systematic treatment of ergodic theory of random transformations i.e., an analysis of composed actions of independent random maps. This set up allows a unified approach to many problems of dynamical systems, products of random matrices and stochastic flows generated by stochastic differential equations.
Ergodic Theory And Topological Dynamics
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Author :
language : en
Publisher: Academic Press
Release Date : 1976-11-15
Ergodic Theory And Topological Dynamics written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976-11-15 with Mathematics categories.
Ergodic Theory and Topological Dynamics
Dynamics Ergodic Theory And Geometry
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Author : Boris Hasselblatt
language : en
Publisher: Cambridge University Press
Release Date : 2007-09-24
Dynamics Ergodic Theory And Geometry written by Boris Hasselblatt 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 2007-09-24 with Mathematics categories.
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.