**Memoirs of the American Mathematical Society**

2010;
130 pp;
Softcover

MSC: Primary 03; 06; 37; 58;
Secondary 55; 57

Print ISBN: 978-0-8218-4870-8

Product Code: MEMO/208/980

List Price: $73.00

AMS Member Price: $43.80

MAA Member Price: $65.70

**Electronic ISBN: 978-1-4704-0594-6
Product Code: MEMO/208/980.E**

List Price: $73.00

AMS Member Price: $43.80

MAA Member Price: $65.70

# Tame Flows

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*Liviu I. Nicolaescu*

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

# Table of Contents

## Tame Flows

- Introduction 19 free
- Chapter 1. Tame spaces 513 free
- Chapter 2. Basic properties and examples of tame flows 1119
- Chapter 3. Some global properties of tame flows 2533
- Chapter 4. Tame Morse flows 2937
- Chapter 5. Tame Morse-Smale flows 4149
- Chapter 6. The gap between two vector subspaces 4553
- Chapter 7. The Whitney and Verdier regularity conditions 5159
- Chapter 8. Smale transversality and Whitney regularity 5563
- Chapter 9. The Conley index 6775
- Chapter 10. Flips/flops and gradient like tame flows 7987
- Chapter 11. Simplicial flows and combinatorial Morse theory 8593
- Chapter 12. Tame currents 97105
- Appendix A. An ``elementary'' proof of the generalized Stokes formula 117125
- Appendix B. On the topology of tame sets 125133
- Bibliography 127135
- Index 129137 free