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A Homology Theory for Smale Spaces - Memoirs of the American Mathematical Society (Paperback)Ian F. Putnam (author)
Paperback 122 Pages / Published: 30/10/2014
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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 finite-to-one 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.
Publisher: American Mathematical Society
Number of pages: 122
Dimensions: 254 x 178 mm
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