---

＜電子ブック＞
Shadowing and Hyperbolicity / by Sergei Yu Pilyugin, Kazuhiro Sakai
(Lecture Notes in Mathematics. ISSN:16179692 ; 2193)

版	1st ed. 2017.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2017
大きさ	XIV, 218 p. 5 illus : online resource
著者標目	*Pilyugin, Sergei Yu author Sakai, Kazuhiro author SpringerLink (Online service)
件　名	LCSH:Dynamical systems FREE:Dynamical Systems
一般注記	Preface -- 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 Focusing 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 HTTP:URL=https://doi.org/10.1007/978-3-319-65184-2

 類似資料