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Homology and Dynamical Systems
John M. Franks
A co-publication of the AMS and CBMS.
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CBMS Regional Conference Series in Mathematics
1982; 120 pp; softcover
Number: 49
Reprint/Revision History:
reprinted 2001, reprinted 2005
ISBN-10: 0-8218-1700-0
ISBN-13: 978-0-8218-1700-1
List Price: US$27
Member Price: US$21.60
All Individuals: US$21.60
Order Code: CBMS/49
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These lectures give a clear and unified exposition of a major area of current research on the connections between dynamics and topology, treating the fundamental problem--what dynamics can occur in a prescribed homological setting--via algebraic chain complexes derived from the unstable manifold decomposition of dynamics.

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"Becoming a standard reference for workers in the field ... Also suitable for advanced graduate students, or for topologists interested in a rapidly growing field of applications."

-- Michael Maller, Mathematical Reviews

Table of Contents

  • Hyperbolic chain recurrent sets
  • Morse gradients
  • Symbolic dynamics for basic sets
  • Smale diffeomorphisms
  • Zeta functions
  • Morse inequalities
  • Morse-Smale diffeomorphisms
  • Morse-Smale flows
  • Smale flows
  • Flows on \(S^3\)
  • Beyond the theme
  • Appendix A. Subshifts as basic sets
  • Appendix B. Constructing fitted diffeomorphisms
  • References
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