Yakov B. Pesin's Books

Dimension Theory in Dynamical Systems

Contemporary Views and Applications

By: Yakov B. Pesin

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Dimension Theory in Dynamical Systems

Contemporary Views and Applications

By: Yakov B. Pesin

The principles of symmetry and self-similarity structure nature's most beautiful creations. For example, they are expressed in fractals, famous for their beautiful but complicated geometric structure, which is the subject of study in dimension theory. And in dynamics the presence of invariant fractals often results in unstable "turbulent-like" motions and is associated with "chaotic" behavior. In this book, Yakov 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. 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.

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Page Count

633

Publisher

University of Chicago Press

Published Date

ISBN 10

0226662233

ISBN 13

9780226662237

Introduction to Smooth Ergodic Theory

Second Edition

By: Luís Barreira,Yakov Pesin

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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.

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Page Count

355

Publisher

American Mathematical Society

Published Date

ISBN 10

1470473070

ISBN 13

9781470473075

Dimension Theory in Dynamical Systems

Contemporary Views and Applications

By: Yakov B. Pesin

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Dimension Theory in Dynamical Systems

Contemporary Views and Applications

By: Yakov B. Pesin

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

633

Publisher

University of Chicago Press

Published Date

ISBN 10

0226662233

ISBN 13

9780226662237

Book's by Yakov B. Pesin

Dimension Theory in Dynamical Systems

Dimension Theory in Dynamical Systems

Introduction to Smooth Ergodic Theory

Introduction to Smooth Ergodic Theory

Dimension Theory in Dynamical Systems

Dimension Theory in Dynamical Systems

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