eBook ISBN:  9781470418977 
Product Code:  MEMO/232/1094.E 
List Price:  $76.00 
MAA Member Price:  $68.40 
AMS Member Price:  $45.60 
eBook ISBN:  9781470418977 
Product Code:  MEMO/232/1094.E 
List Price:  $76.00 
MAA Member Price:  $68.40 
AMS Member Price:  $45.60 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 232; 2014; 122 ppMSC: Primary 37
The author develops a homology theory for Smale spaces, which include the basics sets for an Axiom A diffeomorphism. It is based on two ingredients. The first is an improved version of Bowen's result that every such system is the image of a shift of finite type under a finitetoone factor map. The second is Krieger's dimension group invariant for shifts of finite type. He proves a Lefschetz formula which relates the number of periodic points of the system for a given period to trace data from the action of the dynamics on the homology groups. The existence of such a theory was proposed by Bowen in the 1970s.

Table of Contents

Chapters

Preface

1. Summary

2. Dynamics

3. Dimension groups

4. The complexes of an $s/u$bijective factor map

5. The double complexes of an $s/u$bijective pair

6. A Lefschetz formula

7. Examples

8. Questions


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The author develops a homology theory for Smale spaces, which include the basics sets for an Axiom A diffeomorphism. It is based on two ingredients. The first is an improved version of Bowen's result that every such system is the image of a shift of finite type under a finitetoone factor map. The second is Krieger's dimension group invariant for shifts of finite type. He proves a Lefschetz formula which relates the number of periodic points of the system for a given period to trace data from the action of the dynamics on the homology groups. The existence of such a theory was proposed by Bowen in the 1970s.

Chapters

Preface

1. Summary

2. Dynamics

3. Dimension groups

4. The complexes of an $s/u$bijective factor map

5. The double complexes of an $s/u$bijective pair

6. A Lefschetz formula

7. Examples

8. Questions