000 03741nam a22005775i 4500
001 978-3-319-65184-2
003 DE-He213
005 20210118151949.0
007 cr nn 008mamaa
008 170901s2017 gw | s |||| 0|eng d
020 _a9783319651842
_9978-3-319-65184-2
024 7 _a10.1007/978-3-319-65184-2
_2doi
050 4 _aQA313
072 7 _aPBWR
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBWR
_2thema
082 0 4 _a515.39
_223
082 0 4 _a515.48
_223
100 1 _aPilyugin, Sergei Yu.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aShadowing and Hyperbolicity
_h[electronic resource] /
_cby Sergei Yu Pilyugin, Kazuhiro Sakai.
250 _a1st ed. 2017.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2017.
300 _aXIV, 218 p. 5 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2193
505 0 _aPreface -- 1 Main Definitions 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.
520 _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.
650 0 _aDynamics.
650 0 _aErgodic theory.
650 1 4 _aDynamical Systems and Ergodic Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M1204X
700 1 _aSakai, Kazuhiro.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319651835
776 0 8 _iPrinted edition:
_z9783319651859
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2193
856 4 0 _uhttps://doi.org/10.1007/978-3-319-65184-2
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c452892
_d452892
942 _cEB
506 _aAvailable to subscribing member institutions only. Доступно лише організаціям членам підписки.
506 _fOnline access from local network of NaUOA.
506 _fOnline access with authorization at https://link.springer.com/
506 _fОнлайн-доступ з локальної мережі НаУОА.
506 _fОнлайн доступ з авторизацією на https://link.springer.com/