Smooth Ergodic Theory for Endomorphisms

Min Qian, Jian-Sheng Xie, Shu Zhu

ISBN 10: 3642019536 / ISBN 13: 9783642019531

Editore: Springer-Verlag GmbH, 2009

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Zustand: Sehr gut | Seiten: 277 | Sprache: Englisch | Produktart: Bücher. Codice articolo 5437165/12

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Titolo: Smooth Ergodic Theory for Endomorphisms

Casa editrice: Springer-Verlag GmbH

Data di pubblicazione: 2009

Legatura: Brossura

Condizione: Sehr gut

Descrizione articolo

Riassunto:

Ideal for researchers and graduate students, this volume sets out a general smooth ergodic theory for deterministic dynamical systems generated by non-invertible endomorphisms. Its focus is on the relations between entropy, Lyapunov exponents and dimensions.

Dalla quarta di copertina:

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.