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Smooth Ergodic Theory for Endomorphisms
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 techniq...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2009.
|
| Edición: | 1st ed. 2009. |
| Colección: | Lecture Notes in Mathematics,
1978 |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 100 | 1 | |a Qian, Min. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Smooth Ergodic Theory for Endomorphisms |h [electronic resource] / |c by Min Qian, Jian-Sheng Xie, Shu Zhu. |
| 250 | |a 1st ed. 2009. | ||
| 264 | 1 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg : |b Imprint: Springer, |c 2009. | |
| 300 | |a XIII, 277 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 490 | 1 | |a Lecture Notes in Mathematics, |x 1617-9692 ; |v 1978 | |
| 505 | 0 | |a 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. | |
| 520 | |a 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. | ||
| 650 | 0 | |a Dynamical systems. | |
| 650 | 0 | |a Mechanical engineering. | |
| 650 | 1 | 4 | |a Dynamical Systems. |
| 650 | 2 | 4 | |a Mechanical Engineering. |
| 700 | 1 | |a Xie, Jian-Sheng. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Zhu, Shu. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783642019555 |
| 776 | 0 | 8 | |i Printed edition: |z 9783642019531 |
| 830 | 0 | |a Lecture Notes in Mathematics, |x 1617-9692 ; |v 1978 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-642-01954-8 |z Texto Completo |
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||