03536nam 2200673 450 991048410040332120210218010205.01-282-65580-997866126558073-642-01954-410.1007/978-3-642-01954-8(CKB)1000000000773032(EBL)3064380(SSID)ssj0000320072(PQKBManifestationID)11258293(PQKBTitleCode)TC0000320072(PQKBWorkID)10342773(PQKB)10612356(DE-He213)978-3-642-01954-8(MiAaPQ)EBC3064380(MiAaPQ)EBC6352850(PPN)149048203(EXLCZ)99100000000077303220210218d2009 uy 0engur|n|---|||||txtccrSmooth ergodic theory for endomorphisms /Min Qian, Jian-Sheng Xie, Shu Zhu1st ed. 2009.Berlin, Germany :Springer,[2009]©20091 online resource (291 p.)Lecture notes in mathematics ;1978Description based upon print version of record.3-642-01953-6 3-642-01955-2 Includes bibliographical references (pages [271]-274) and index.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.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.Lecture notes in mathematics (Springer-Verlag) ;1978.Endomorphisms (Group theory)Ergodic theoryEndomorphisms (Group theory)Ergodic theory.515.39MAT 344fstubSI 850rvkQian Min1927-61002Xie Jian-shengZhu Shu1964-MiAaPQMiAaPQMiAaPQBOOK9910484100403321Smooth ergodic theory for endomorphisms2830863UNINA