Memoirs of the American Mathematical Society 2010; 130 pp; softcover Volume: 208 ISBN10: 0821848704 ISBN13: 9780821848708 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. Table of Contents  Introduction
 Tame spaces
 Basic properties and examples of tame flows
 Some global properties of tame flows
 Tame Morse flows
 Tame MorseSmale 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
