Differentiable dynamical systems : an introduction to structural stability and hyperbolicity
著者
書誌事項
Differentiable dynamical systems : an introduction to structural stability and hyperbolicity
（Graduate studies in mathematics, v. 173）
American Mathematical Society, c2016
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注記
Includes bibliographical references (p. 181-187) and index
内容説明・目次
内容説明
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 -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.
目次
Basics of dynamical systems
Hyperbolic fixed points
Horseshoes, toral automorphisms, and solenoids
Hyperbolic sets
Axiom A, no-cycle condition, and -stability
Quasi-hyperbolicity and linear transversality
Bibliography
Index
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