The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center
We prove that if f is a partially hyperbolic diffeomorphism on the compact manifold M with one dimensional center bundle, then the logarithm of the spectral radius of the map induced by f on the real homology groups of M is smaller or equal to the topological entropy of f. This is a particular case...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2008 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:44117 |
| Online Access: | https://ddd.uab.cat/record/44117 |
| Access Level: | Open access |
| Keyword: | Entropia Difeomorfismes |
| Summary: | We prove that if f is a partially hyperbolic diffeomorphism on the compact manifold M with one dimensional center bundle, then the logarithm of the spectral radius of the map induced by f on the real homology groups of M is smaller or equal to the topological entropy of f. This is a particular case of the Shub's entropy conjecture, which claims that the same conclusion should be true for any C1 map on any compact manifold. |
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