Smooth Ergodic Theory for Endomorphisms / by Min Qian, Jian-Sheng Xie, Shu Zhu
(Lecture Notes in Mathematics ; 1978)
| データ種別 | 電子ブック |
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| 出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg |
| 出版年 | 2009 |
| 本文言語 | 英語 |
| 大きさ | XIII, 277 p : online resource |
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| 内容注記 | 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 |
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| 一般注記 | 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 |
| 著者標目 | *Qian, Min author Xie, Jian-Sheng author Zhu, Shu author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Dynamics LCSH:Ergodic theory LCSH:Mechanical engineering FREE:Mathematics FREE:Dynamical Systems and Ergodic Theory FREE:Mechanical Engineering |
| 分 類 | DC23:515.39 DC23:515.48 |
| 巻冊次 | ISBN:9783642019548 
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| ISBN | 9783642019548 |
| URL | http://dx.doi.org/10.1007/978-3-642-01954-8 |
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