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.

Readership

Reviews

"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