The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center |
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Authors: | Radu Saghin Zhihong Xia |
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Institution: | aCentre de Recerca Matematica, Apartat 50, Bellaterra, Barcelona 08193, Spain;bDepartment of Mathematics, Northwestern University, Evanston, IL 60208, USA |
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Abstract: | 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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Keywords: | Entropy conjecture Partially hyperbolic diffeomorphisms Volume growth |
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