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Anotace knihy

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.

Parametry knihy

Zařazení knihy Knihy v angličtině Technology, engineering, agriculture Mechanical engineering & materials Mechanical engineering

• Plný název: Smooth Ergodic Theory for Endomorphisms
• Autor: Quian Min, Jian-Sheng Xie, Shu Zhu
• Jazyk: Angličtina
• Vazba: Brožovaná
• Počet stran: 277
• EAN: 9783642019531
• ISBN: 3642019536
• ID: 01649817
• Nakladatelství: Springer, Berlin
• Hmotnost: 478 g
• Rozměry: 235 × 154 × 15 mm
• Rok vydání: 2009

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