Ya. B. Pesin's Books

Introduction to Smooth Ergodic Theory

Second Edition

By: Luís Barreira,Yakov Pesin

Write a review Read reviews Take a Quiz Solve Book Puzzle

Introduction to Smooth Ergodic Theory

Second Edition

By: Luís Barreira,Yakov Pesin

This book is the first comprehensive introduction to smooth ergodic theory. It consists of two parts: the first introduces the core of the theory and the second discusses more advanced topics. In particular, the book describes the general theory of Lyapunov exponents and its applications to the stability theory of differential equations, the concept of nonuniform hyperbolicity, stable manifold theory (with emphasis on absolute continuity of invariant foliations), and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. A detailed description of all the basic examples of conservative systems with nonzero Lyapunov exponents, including the geodesic flows on compact surfaces of nonpositive curvature, is also presented. There are more than 80 exercises. The book is aimed at graduate students specializing in dynamical systems and ergodic theory as well as anyone who wishes to get a working knowledge of smooth ergodic theory and to learn how to use its tools. It can also be used as a source for special topics courses on nonuniform hyperbolicity. The only prerequisite for using this book is a basic knowledge of real analysis, measure theory, differential equations, and topology, although the necessary background definitions and results are provided. In this second edition, the authors improved the exposition and added more exercises to make the book even more student-oriented. They also added new material to bring the book more in line with the current research in dynamical systems.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

355

Publisher

American Mathematical Society

Published Date

ISBN 10

1470473070

ISBN 13

9781470473075

Nonuniform Hyperbolicity

Dynamics of Systems with Nonzero Lyapunov Exponents

By: Luis Barreira

Write a review Read reviews Take a Quiz Solve Book Puzzle

Nonuniform Hyperbolicity

Dynamics of Systems with Nonzero Lyapunov Exponents

By: Luis Barreira

A self-contained, comprehensive account of modern smooth ergodic theory, the mathematical foundation of deterministic chaos.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

490

Published Date

ISBN 10

1107104009

ISBN 13

9781107104006

Dynamical Systems, Ergodic Theory and Applications

By: L.A. Bunimovich,Ya.G. Sinai,S.G. Dani,R.L. Dobrushin,M.V. Jakobson,I.P. Kornfeld,N.B. Maslova,Ya.B. Pesin,J. Smillie,Yu.M. Sukhov,A.M. Vershik

Write a review Read reviews Take a Quiz Solve Book Puzzle

Dynamical Systems, Ergodic Theory and Applications

By: L.A. Bunimovich,Ya.G. Sinai,S.G. Dani,R.L. Dobrushin,M.V. Jakobson,I.P. Kornfeld,N.B. Maslova,Ya.B. Pesin,J. Smillie,Yu.M. Sukhov,A.M. Vershik

This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, familiarizes the reader with the fundamental ideas and results of modern ergodic theory and its applications to dynamical systems and statistical mechanics. The enlarged and revised second edition adds two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

460

Publisher

Springer

Published Date

ISBN 10

364208561X

ISBN 13

9783642085611

Dimension Theory in Dynamical Systems

Contemporary Views and Applications

By: Ya. B. Pesin

Write a review Read reviews Take a Quiz Solve Book Puzzle

Dimension Theory in Dynamical Systems

Contemporary Views and Applications

By: Ya. B. Pesin

In this book, Yakov B. Pesin introduces a new area of research that has recently appeared in the interface between dimension theory and the theory of dynamical systems. Focusing on invariant fractals and their influence on stochastic properties of systems, Pesin provides a comprehensive and systematic treatment of modern dimension theory in dynamical systems, summarizes the current state of research, and describes the most important accomplishments of this field. Topics include, but are not restricted to, the general concept of dimension; the dimension interpretation of some well-known invariants of dynamical systems, such as topological and measure-theoretic entropies; formulas of dimension of some well-known hyperbolic invariant sets, such as Julia sets, horseshoes, and solenoids; mathematical analysis of dimensions that are most often used in applied research, such as correlation and information dimensions; and mathematical theory of invariant multifractals. Pesin's synthesis of these subjects of broad current research interest will be appreciated both by advanced mathematicians and by a wide range of scientists who depend upon mathematical modeling of dynamical processes. The book can also be used as a text for a special topics course in the theory of dynamical systems and dimension theory.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

326

Publisher

University of Chicago Press

Published Date

ISBN 10

0226662217

ISBN 13

9780226662213

Lectures on Partial Hyperbolicity and Stable Ergodicity

By: Ya. B. Pesin

Write a review Read reviews Take a Quiz Solve Book Puzzle

Lectures on Partial Hyperbolicity and Stable Ergodicity

By: Ya. B. Pesin

This book is an introduction to the modern theory of partial hyperbolicity with applications to stable ergodicity theory of smooth dynamical systems. It provides a systematic treatment of the theory and describes all the basic concepts and major results obtained in the area since its creation in the early 1970s. It can be used as a textbook for a graduate student course and is also of interest to professional mathematicians.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

134

Publisher

European Mathematical Society

Published Date

ISBN 10

3037190035

ISBN 13

9783037190036

Lectures on Fractal Geometry and Dynamical Systems

By: Ya. B. Pesin,Vaughn Climenhaga

Write a review Read reviews Take a Quiz Solve Book Puzzle

Lectures on Fractal Geometry and Dynamical Systems

By: Ya. B. Pesin,Vaughn Climenhaga

Both fractal geometry and dynamical systems have a long history of development and have provided fertile ground for many great mathematicians and much deep and important mathematics. These two areas interact with each other and with the theory of chaos in a fundamental way: many dynamical systems (even some very simple ones) produce fractal sets, which are in turn a source of irregular 'chaotic' motions in the system. This book is an introduction to these two fields, with an emphasis on the relationship between them. The first half of the book introduces some of the key ideas in fractal geometry and dimension theory - Cantor sets, Hausdorff dimension, box dimension - using dynamical notions whenever possible, particularly one-dimensional Markov maps and symbolic dynamics. Various techniques for computing Hausdorff dimension are shown, leading to a discussion of Bernoulli and Markov measures and of the relationship between dimension, entropy, and Lyapunov exponents. In the second half of the book some examples of dynamical systems are considered and various phenomena of chaotic behaviour are discussed, including bifurcations, hyperbolicity, attractors, horseshoes, and intermittent and persistent chaos. These phenomena are naturally revealed in the course of our study of two real models from science - the FitzHugh - Nagumo model and the Lorenz system of differential equations. This book is accessible to undergraduate students and requires only standard knowledge in calculus, linear algebra, and differential equations. Elements of point set topology and measure theory are introduced as needed. This book is a result of the MASS course in analysis at Penn State University in the fall semester of 2008.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

334

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821848895

ISBN 13

9780821848890

Book's by Ya. B. Pesin

Introduction to Smooth Ergodic Theory

Introduction to Smooth Ergodic Theory

Nonuniform Hyperbolicity

Nonuniform Hyperbolicity

Dynamical Systems, Ergodic Theory and Applications

Dynamical Systems, Ergodic Theory and Applications

Dimension Theory in Dynamical Systems

Dimension Theory in Dynamical Systems

Lectures on Partial Hyperbolicity and Stable Ergodicity

Lectures on Partial Hyperbolicity and Stable Ergodicity

Lectures on Fractal Geometry and Dynamical Systems

Lectures on Fractal Geometry and Dynamical Systems

Username

Password

Username

Password

Password again

Birthday

Email