Format:
Online-Ressource (digital)
ISBN:
9783642019548
Series Statement:
Lecture Notes in Mathematics 1978
Content:
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
Content:
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
Note:
Includes bibliographical references (p. 271-274) and index
,
""Preface""; ""Contents""; ""Chapter I Preliminaries""; ""Chapter II Margulis-Ruelle Inequality""; ""Chapter III Expanding Maps""; ""Chapter IV Axiom A Endomorphisms""; ""Chapter V Unstable and Stable Manifolds for Endomorphisms""; ""Chapter VI Pesin�s Entropy Formula for Endomorphisms""; ""Chapter VII SRB Measures and Pesin�s Entropy Formula for Endomorphisms""; ""Chapter VIII Ergodic Property of Lyapunov Exponents""; ""Chapter IX Generalized Entropy Formula""; ""Chapter X Exact Dimensionality of Hyperbolic Measures""
,
""Appendix A Entropy Formula of Pesin Type for One-sided Stationary Random Maps""""Appendix B Large Deviations in Axiom A Endomorphisms""; ""References""; ""Index""
Additional Edition:
ISBN 9783642019531
Additional Edition:
Buchausg. u.d.T. Qian, Min, 1970 - Smooth ergodic theory for endomorphisms Berlin : Springer, 2009 ISBN 9783642019531
Language:
English
Subjects:
Mathematics
Keywords:
Dynamisches System
;
Endomorphismus
;
Ergodentheorie
;
Dynamisches System
;
Endomorphismus
;
Ergodentheorie
DOI:
10.1007/978-3-642-01954-8
URL:
Volltext
(lizenzpflichtig)
Author information:
Qian, Min 1970-
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