000			02020nam a22002535i 4500
001			138242
003			ISI Library, Kolkata
005			20180328122743.0
008			170728s2017 nyu 000 0 eng
020			_a9783319651835 (alk. paper)
040			_aISI Library
082	0	4	_a515.3535 _223 _bP643
100	1		_aPilyugin, Sergei Yu., _eauthor
245	1	0	_aShadowing and hyperbolicity / _cSergei Yu. Pilyugin and Kazuhiro Sakai.
260			_aCham : _bSpringer, _c2017.
300			_axiv, 216 pages : _billustrations ; _c24 cm.
490	0		_aLecture notes in mathematics ; _v2193.
504			_aInclude index and bibliographical references and index.
505	0		_a1. Main Definitions and Basic Results.- 2. Lipschitz and Holder Shadowing and Structural Stability.- 3. C1 interiors of Sets of Systems with Various Shadowing Properties.- 4. Chain Transitive Sets and Shadowing.- References.- Index.
520			_aThis 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	_aHyperbolic equations.
700	1		_aSakai, Kazuhiro, _eauthor
942			_2ddc _cBK
999			_c424538 _d424538