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Smooth Ergodic Theory for Endomorphisms

Name: Smooth Ergodic Theory for Endomorphisms
Brand: Springer, Berlin
SKU: 01649817
Price: 55.67 EUR
Availability: InStock
Author: Quian Min
ISBN: 9783642019531

Quian Min

Jian-Sheng Xie

Shu Zhu

Jazyk

Angličtina

Kniha Brožovaná

Libristo kód: 01649817

Nakladateľstvo Springer, Berlin, november 2008

This volume presents a general smooth ergodic theory for deterministic dynamical systems generated b... Celý popis

Libristo kód: 01649817

135 b

55.67 €

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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 attack 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.