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The General Topology of Dynamical Systems
Ethan Akin
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Graduate Studies in Mathematics
1993; 261 pp; softcover
Volume: 1
ISBN-10: 0-8218-4932-8
ISBN-13: 978-0-8218-4932-3
List Price: US$44
Member Price: US$35.20
Order Code: GSM/1.S
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See also:

Dynamical Systems and Population Persistence - Hal L Smith and Horst R Thieme

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 graduate-level 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 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.

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
  • 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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