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portada Smooth Ergodic Theory for Endomorphisms
Type
Physical Book
Publisher
Author
Year
2009
Language
English
Pages
300
Format
Paperback
Dimensions
23.4x15.6x1.6 cm
Weight
0.42 kg.
ISBN
3642019536
ISBN13
9783642019531
Edition No.
2009
Categories

Smooth Ergodic Theory for Endomorphisms

Qian Min,Xie Jian-Sheng,Zhu Shu (Author) · Springer · Paperback

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

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Synopsis "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 anddimensions. The authors make extensive use of the combination of the inverse limit space technique and the techniques developed to attack random dynamical systems. The most interesting results in this book are (1) theequivalence 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 theexact-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 classicalresults 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 ofballs of certain properties, which are extensively used in Chapters IX and X.

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