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Ergodic Theory and Dynamical Systems

2016-11-10 Mathematics
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Release : 2016-11-10
Genre : Mathematics
Kind : eBook
Book Rating : 876/5 ( reviews)

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Book Synopsis Ergodic Theory and Dynamical Systems by : Yves Coudène

Download or read book Ergodic Theory and Dynamical Systems written by Yves Coudène. This book was released on 2016-11-10. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topics in Dynamics and Ergodic Theory

2003-12-08 Mathematics
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Release : 2003-12-08
Genre : Mathematics
Kind : eBook
Book Rating : 652/5 ( reviews)

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Book Synopsis Topics in Dynamics and Ergodic Theory by : Sergey Bezuglyi

Download or read book Topics in Dynamics and Ergodic Theory written by Sergey Bezuglyi. This book was released on 2003-12-08. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topics in Ergodic Theory

2004-06-03 Mathematics
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Release : 2004-06-03
Genre : Mathematics
Kind : eBook
Book Rating : 901/5 ( reviews)

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Book Synopsis Topics in Ergodic Theory by : William Parry

Download or read book Topics in Ergodic Theory written by William Parry. This book was released on 2004-06-03. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to topics and examples of ergodic theory, a central area of pure mathematics.

Ergodic Theory

2010-09-11 Mathematics
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Release : 2010-09-11
Genre : Mathematics
Kind : eBook
Book Rating : 215/5 ( reviews)

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Book Synopsis Ergodic Theory by : Manfred Einsiedler

Download or read book Ergodic Theory written by Manfred Einsiedler. This book was released on 2010-09-11. Available in PDF, EPUB and Kindle. Book excerpt: 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 Dynamics

2021-01-28 Mathematics
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Release : 2021-01-28
Genre : Mathematics
Kind : eBook
Book Rating : 421/5 ( reviews)

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Book Synopsis Ergodic Dynamics by : Jane Hawkins

Download or read book Ergodic Dynamics written by Jane Hawkins. This book was released on 2021-01-28. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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