Smooth Ergodic Theory for Endomorphisms / by Min Qian, Jian-Sheng Xie, Shu Zhu.

Format:

Book

Author/Creator:

Qian, Min, author.

Xie, Jian-sheng, author.

Zhu, Shu, 1964- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1978.

Lecture Notes in Mathematics, 0075-8434 ; 1978

Language:

English

Subjects (All):

Differentiable dynamical systems.

Mechanical engineering.

Dynamical Systems and Ergodic Theory.

Mechanical Engineering.

Local Subjects:

Dynamical Systems and Ergodic Theory.

Mechanical Engineering.

Physical Description:

1 online resource (XIII, 277 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.

System Details:

text file PDF

Summary:

This volume presents a general smooth ergodic theory for deterministic dynamical systems generated by non-invertible endomorphisms, mainly concerning the relations between entropy, Lyapunov exponents and dimensions. The authors make extensive use of the combination of the inverse limit space technique and the techniques developed to tackle random dynamical systems. The most interesting results in this book are (1) the equivalence between the SRB property and Pesin's entropy formula; (2) the generalized Ledrappier-Young entropy formula; (3) exact-dimensionality for weakly hyperbolic diffeomorphisms and for expanding maps. The proof of the exact-dimensionality for weakly hyperbolic diffeomorphisms seems more accessible than that of Barreira and others It also inspires the authors to argue to what extent the famous Eckmann-Ruelle conjecture and many other classical results for diffeomorphisms and for flows hold true. After a careful reading of the book, one can systematically learn the Pesin theory for endomorphisms as well as the typical tricks played in the estimation of the number of balls of certain properties, which are extensively used in Chapters IX and X.

Contents:

Preliminaries

Margulis-Ruelle Inequality

Expanding Maps

Axiom A Endomorphisms

Unstable and Stable Manifolds for Endomorphisms

Pesin#x2019;s Entropy Formula for Endomorphisms

SRB Measures and Pesin#x2019;s Entropy Formula for Endomorphisms

Ergodic Property of Lyapunov Exponents

Generalized Entropy Formula

Exact Dimensionality of Hyperbolic Measures.

Other Format:

Printed edition:

ISBN:

9783642019548

Access Restriction:

Restricted for use by site license.