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- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1978)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
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)Authors and Affiliations
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Dept. Mathematics, Peking University, Beijing, China, People's Republic
Min Qian
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School of Mathematical Sciences, Fudan University, Shanghai, China, People's Republic
Jian-Sheng Xie
Bibliographic Information
Book Title: Smooth Ergodic Theory for Endomorphisms
Authors: Min Qian, Jian-Sheng Xie, Shu Zhu
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-642-01954-8
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2009
Softcover ISBN: 978-3-642-01953-1Published: 02 September 2009
eBook ISBN: 978-3-642-01954-8Published: 07 July 2009
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XIII, 277
Topics: Dynamical Systems and Ergodic Theory, Mechanical Engineering