LEADER 03534nam 2200673 450 001 996466770403316 005 20210218010205.0 010 $a1-282-65580-9 010 $a9786612655807 010 $a3-642-01954-4 024 7 $a10.1007/978-3-642-01954-8 035 $a(CKB)1000000000773032 035 $a(EBL)3064380 035 $a(SSID)ssj0000320072 035 $a(PQKBManifestationID)11258293 035 $a(PQKBTitleCode)TC0000320072 035 $a(PQKBWorkID)10342773 035 $a(PQKB)10612356 035 $a(DE-He213)978-3-642-01954-8 035 $a(MiAaPQ)EBC3064380 035 $a(MiAaPQ)EBC6352850 035 $a(PPN)149048203 035 $a(EXLCZ)991000000000773032 100 $a20210218d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSmooth ergodic theory for endomorphisms /$fMin Qian, Jian-Sheng Xie, Shu Zhu 205 $a1st ed. 2009. 210 1$aBerlin, Germany :$cSpringer,$d[2009] 210 4$dİ2009 215 $a1 online resource (291 p.) 225 1 $aLecture notes in mathematics ;$v1978 300 $aDescription based upon print version of record. 311 $a3-642-01953-6 311 $a3-642-01955-2 320 $aIncludes bibliographical references (pages [271]-274) and index. 327 $aPreliminaries -- 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. 330 $aThis volume presents a general smooth ergodic theory for deterministic dynamical systems generated by non-invertible endomorphisms, mainly concerning the relations between entropy, Lyapunov exponents and dimensions. The authors make extensive use of the combination of the inverse limit space technique and the techniques developed to tackle random dynamical systems. The most interesting results in this book are (1) the equivalence between the SRB property and Pesin?s entropy formula; (2) the generalized Ledrappier-Young entropy formula; (3) exact-dimensionality for weakly hyperbolic diffeomorphisms and for expanding maps. The proof of the exact-dimensionality for weakly hyperbolic diffeomorphisms seems more accessible than that of Barreira et al. It also inspires the authors to argue to what extent the famous Eckmann-Ruelle conjecture and many other classical results for diffeomorphisms and for flows hold true. After a careful reading of the book, one can systematically learn the Pesin theory for endomorphisms as well as the typical tricks played in the estimation of the number of balls of certain properties, which are extensively used in Chapters IX and X. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1978. 606 $aEndomorphisms (Group theory) 606 $aErgodic theory 615 0$aEndomorphisms (Group theory) 615 0$aErgodic theory. 676 $a515.39 686 $aMAT 344f$2stub 686 $aSI 850$2rvk 700 $aQian$b Min$f1927-$061002 702 $aXie$b Jian-sheng 702 $aZhu$b Shu$f1964- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466770403316 996 $aSmooth ergodic theory for endomorphisms$92830863 997 $aUNISA