LEADER 03048nam 22005175 450 001 9910257379003321 005 20200705130304.0 010 $a3-319-65184-6 024 7 $a10.1007/978-3-319-65184-2 035 $a(CKB)4100000000587417 035 $a(DE-He213)978-3-319-65184-2 035 $a(MiAaPQ)EBC5595210 035 $a(PPN)204533279 035 $a(EXLCZ)994100000000587417 100 $a20170901d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aShadowing and Hyperbolicity /$fby Sergei Yu Pilyugin, Kazuhiro Sakai 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XIV, 218 p. 5 illus.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2193 300 $aIncludes index. 311 $a3-319-65183-8 327 $aPreface -- 1 Main De?nitions and Basic Results -- Lipschitz and H¨older Shadowing and Structural Stability -- 3 C1 interiors of Sets of Systems with Various Shadowing Properties -- 4 Chain Transitive Sets and Shadowing -- References -- Index. 330 $aFocusing on the theory of shadowing of approximate trajectories (pseudotrajectories) of dynamical systems, this book surveys recent progress in establishing relations between shadowing and such basic notions from the classical theory of structural stability as hyperbolicity and transversality. Special attention is given to the study of "quantitative" shadowing properties, such as Lipschitz shadowing (it is shown that this property is equivalent to structural stability both for diffeomorphisms and smooth flows), and to the passage to robust shadowing (which is also equivalent to structural stability in the case of diffeomorphisms, while the situation becomes more complicated in the case of flows). Relations between the shadowing property of diffeomorphisms on their chain transitive sets and the hyperbolicity of such sets are also described. The book will allow young researchers in the field of dynamical systems to gain a better understanding of new ideas in the global qualitative theory. It will also be of interest to specialists in dynamical systems and their applications. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2193 606 $aDynamics 606 $aErgodic theory 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 615 0$aDynamics. 615 0$aErgodic theory. 615 14$aDynamical Systems and Ergodic Theory. 676 $a515.352 700 $aPilyugin$b Sergei Yu$4aut$4http://id.loc.gov/vocabulary/relators/aut$060268 702 $aSakai$b Kazuhiro$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910257379003321 996 $aShadowing and Hyperbolicity$92148589 997 $aUNINA