Shadowing and hyperbolicity / Sergei Yu. Pilyugin and Kazuhiro Sakai.
Material type:
TextSeries: Lecture notes in mathematics ; 2193.Publication details: Cham : Springer, 2017.Description: xiv, 216 pages : illustrations ; 24 cmISBN: - 9783319651835 (alk. paper)
- 515.3535 23 P643
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 515.3535 P643 (Browse shelf(Opens below)) | Available | 138242 |
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| 515.3533 N364 Direct methods in the theory of elliptic equations | 515.3533 So682 Hangzhou lectures on eigenfunctions of the Laplacian / | 515.3535 L425 Hyperbolic partial differential equations | 515.3535 P643 Shadowing and hyperbolicity / | 515.354 B114 Transcendental functions; satisfying nonhomogeneous linear differential equations | 515.354 B671 Differential equations with linear algebra | 515.354 C762 Linear differential equations and control |
Include index and bibliographical references and index.
1. 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.
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.
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