A Homology Theory for Smale Spaces
Author | : Ian Fraser Putnam |
Publisher | : |
Total Pages | : 122 |
Release | : 2014 |
ISBN-10 | : 1470418975 |
ISBN-13 | : 9781470418977 |
Rating | : 4/5 (977 Downloads) |
Download or read book A Homology Theory for Smale Spaces written by Ian Fraser Putnam and published by . This book was released on 2014 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop 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. We prove 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 1970's.