Lecture Notes in Mathematics
cover

Smooth Ergodic Theory for Endomorphisms

Authors: Qian, Min, Xie, Jian-Sheng, Zhu, Shu

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About this book

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 et al. 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.

Reviews

From the reviews:

“In the useful monograph under review the authors intend to assemble several topics in the classic ergodic theory of deterministic endomorphisms gathering the most important results available until the present time. … should be of interest to mathematicians, postgraduate students and physicists working on this field.” (Mário Bessa, Mathematical Reviews, Issue 2010 m)

Table of contents (10 chapters)

Table of contents (10 chapters)
  • Preliminaries

    QUIAN, Min (et al.)

    Pages 1-8

  • Margulis-Ruelle Inequality

    QUIAN, Min (et al.)

    Pages 9-13

  • Expanding Maps

    QUIAN, Min (et al.)

    Pages 15-26

  • Axiom A Endomorphisms

    QUIAN, Min (et al.)

    Pages 27-44

  • Unstable and Stable Manifolds for Endomorphisms

    QUIAN, Min (et al.)

    Pages 45-86

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-3-642-01954-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-642-01953-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Smooth Ergodic Theory for Endomorphisms
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1978
Copyright
2009
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-01954-8
DOI
10.1007/978-3-642-01954-8
Softcover ISBN
978-3-642-01953-1
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIII, 277
Topics