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Tame Flows
Liviu I. Nicolaescu, University of Notre Dame, IN
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Memoirs of the American Mathematical Society
2010; 130 pp; softcover
Volume: 208
ISBN-10: 0-8218-4870-4
ISBN-13: 978-0-8218-4870-8
List Price: US$69 Individual Members: US$41.40
Institutional Members: US\$55.20
Order Code: MEMO/208/980

The tame flows are "nice" flows on "nice" spaces. The nice (tame) sets are the pfaffian sets introduced by Khovanski, and a flow $$\Phi: \mathbb{R}\times X\rightarrow X$$ on pfaffian set $$X$$ is tame if the graph of $$\Phi$$ is a pfaffian subset of $$\mathbb{R}\times X\times X$$. Any compact tame set admits plenty tame flows. The author proves that the flow determined by the gradient of a generic real analytic function with respect to a generic real analytic metric is tame.

• Introduction
• Tame spaces
• Basic properties and examples of tame flows
• Some global properties of tame flows
• Tame Morse flows
• Tame Morse-Smale flows
• The gap between two vector subspaces
• The Whitney and Verdier regularity conditions
• Smale transversality and Whitney regularity
• The Conley index
• Flips/flops and gradient like tame flows
• Simplicial flows and combinatorial Morse theory
• Tame currents
• Appendix A. An "elementary" proof of the generalized Stokes formula
• Appendix B. On the topology of tame sets
• Bibliography
• Index