Graduate Studies in Mathematics 1993; 261 pp; softcover Volume: 1 ISBN10: 0821849328 ISBN13: 9780821849323 List Price: US$44 Member Price: US$35.20 Order Code: GSM/1.S
 It contains a wealth of information concerning topological dynamics, most of which has not appeared before in such an organization and presentation. It offers to a graduatelevel student a very comprehensive overview on the basic concepts in the theory of dynamical systems. Zentralblatt MATH No other single text has heretofore presented such a unified treatment of these topological ideas at this level of generality. Mathematical Reviews 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 preexisting 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 pointset 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. Readership Graduate students and research mathematicians interested in dynamical systems. Table of Contents  Introduction: Gradient systems
 Closed relations and their dynamic extensions
 Invariant sets and Lyapunov functions
 Attractors and basic sets
 Mappingsinvariant 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
 Examplescircles, simplex, and symbols
 Fixed points
 Hyperbolic sets and axiom A homeomorphisms
 Historical remarks
 References
 Subject index
