<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. |
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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 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783319651842 |
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EB00211065 |
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