The general topology of dynamical systems
著者
書誌事項
The general topology of dynamical systems
（Graduate studies in mathematics, v. 1）
American Mathematical Society, c1993
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注記
Bibliography: p. 255-258
Includes index
内容説明・目次
内容説明
Topology, the foundation of modern analysis, arose historically as a way to organize ideas like compactness and connectedness which had emerged from analysis. Similarly, recent work in dynamical systems theory has both highlighted certain topics in the pre-existing subject of topological dynamics (such as the construction of Lyapunov functions and various notions of stability) and also generated new concepts and results (such as attractors, chain recurrence, and basic sets).This book collects these results, both old and new, and organizes them into a natural foundation for all aspects of dynamical systems theory. No existing book is comparable in content or scope. Requiring background in point-set topology and some degree of 'mathematical sophistication', Akin's book serves as an excellent textbook for a graduate course in dynamical systems theory. In addition, Akin's reorganization of previously scattered results makes this book of interest to mathematicians and other researchers who use dynamical systems in their work.
目次
Introduction: Gradient systems Closed relations and their dynamic extensions Invariant sets and Lyapunov functions Attractors and basic sets Mappings--invariant subsets and transitivity concepts Computation of the chain recurrent set Chain recurrence and Lyapunov functions for flows Topologically robust properties of dynamical systems Invariant measures for mappings Examples--circles, simplex, and symbols Fixed points Hyperbolic sets and axiom a homeomorphisms Historical remarks References Subject index.
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