Cargando…
A homology theory for smale spaces
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....
| Autor principal: | |
|---|---|
| Lenguaje: | eng |
| Publicado: |
American Mathematical Society
2014
|
| Materias: | |
| Acceso en línea: | http://cds.cern.ch/record/2623078 |
| _version_ | 1780958656389447680 |
|---|---|
| author | Putnam, Ian F |
| author_facet | Putnam, Ian F |
| author_sort | Putnam, Ian F |
| collection | CERN |
| description | 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. |
| id | cern-2623078 |
| institution | Organización Europea para la Investigación Nuclear |
| language | eng |
| publishDate | 2014 |
| publisher | American Mathematical Society |
| record_format | invenio |
| spelling | cern-26230782021-04-21T18:47:43Zhttp://cds.cern.ch/record/2623078engPutnam, Ian FA homology theory for smale spacesMathematical Physics and MathematicsThe 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.American Mathematical Societyoai:cds.cern.ch:26230782014 |
| spellingShingle | Mathematical Physics and Mathematics Putnam, Ian F A homology theory for smale spaces |
| title | A homology theory for smale spaces |
| title_full | A homology theory for smale spaces |
| title_fullStr | A homology theory for smale spaces |
| title_full_unstemmed | A homology theory for smale spaces |
| title_short | A homology theory for smale spaces |
| title_sort | homology theory for smale spaces |
| topic | Mathematical Physics and Mathematics |
| url | http://cds.cern.ch/record/2623078 |
| work_keys_str_mv | AT putnamianf ahomologytheoryforsmalespaces AT putnamianf homologytheoryforsmalespaces |