Differentiable dynamical systems : an introduction to structural stability and hyperbolicity / Lan Wen.
Material type:
TextSeries: Graduate studies in mathematics ; 173.Publication details: Providence : American Mathematical Society, ©2016.Description: xi, 192 pages : illustrations ; 26 cmISBN: - 9781470427993 (hbk. : acidfree paper)
- 515.39 23 W467
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 515.39 W467 (Browse shelf(Opens below)) | Available | 137966 |
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| 515.39 M899 Notes on dynamical systems | 515.39 P871 Geometric theory of discrete nonautonomous dynamical systems | 515.39 R662 Dimensions, embeddings, and attractors | 515.39 W467 Differentiable dynamical systems : | 515.392 Am518 Stabilization of elastic systems by collocated feedback / | 515.392 H752 Introduction to perturbation methods / | 515.392 K86 Optimization in function spaces |
Includes bibliographical references and index.
1. Basics of dynamical systems --
2. Hyperbolic fixed points --
3. Horseshoes, toral automorphisms, and solenoids --
4. Hyperbolic sets --
5. Axiom A, no-cycle condition, and Ω-stability --
6. Quasi-hyperbolicity and linear transversality --
Bibliography --
Index.
This is a graduate text in differentiable dynamical systems. It focuses on structural stability and hyperbolicity, a topic that is central to the field. Starting with the basic concepts of dynamical systems, analyzing the historic systems of the Smale horseshoe, Anosov toral automorphisms, and the solenoid attractor, the book develops the hyperbolic theory first for hyperbolic fixed points and then for general hyperbolic sets. The problems of stable manifolds, structural stability, and shadowing property are investigated, which lead to a highlight of the book, the Ω-stability theorem of Smale.While the content is rather standard, a key objective of the book is to present a thorough treatment for some tough material that has remained an obstacle to teaching and learning the subject matter. The treatment is straightforward and hence could be particularly suitable for self-study.
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