eBook ISBN:  9781470405946 
Product Code:  MEMO/208/980.E 
List Price:  $73.00 
MAA Member Price:  $65.70 
AMS Member Price:  $43.80 
eBook ISBN:  9781470405946 
Product Code:  MEMO/208/980.E 
List Price:  $73.00 
MAA Member Price:  $65.70 
AMS Member Price:  $43.80 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 208; 2010; 130 ppMSC: Primary 03; 06; 37; 58; Secondary 55
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

Chapters

Introduction

1. Tame spaces

2. Basic properties and examples of tame flows

3. Some global properties of tame flows

4. Tame Morse flows

5. Tame MorseSmale flows

6. The gap between two vector subspaces

7. The Whitney and Verdier regularity conditions

8. Smale transversality and Whitney regularity

9. The Conley index

10. Flips/flops and gradient like tame flows

11. Simplicial flows and combinatorial Morse theory

12. Tame currents

A. An “elementary” proof of the generalized Stokes formula

B. On the topology of tame sets


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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.

Chapters

Introduction

1. Tame spaces

2. Basic properties and examples of tame flows

3. Some global properties of tame flows

4. Tame Morse flows

5. Tame MorseSmale flows

6. The gap between two vector subspaces

7. The Whitney and Verdier regularity conditions

8. Smale transversality and Whitney regularity

9. The Conley index

10. Flips/flops and gradient like tame flows

11. Simplicial flows and combinatorial Morse theory

12. Tame currents

A. An “elementary” proof of the generalized Stokes formula

B. On the topology of tame sets