$\mathcal{C}^{2}$ surface diffeomorphisms have symbolic extensions |
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Authors: | David Burguet |
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Institution: | 1.CMLA-ENS Cachan,Cachan Cedex,France |
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Abstract: | We prove that C2\mathcal{C}^{2} surface diffeomorphisms have symbolic extensions, i.e. topological extensions which are subshifts over a finite alphabet.
Following the strategy of Downarowicz and Maass (Invent. Math. 176:617–636, 2009) we bound the local entropy of ergodic measures in terms of Lyapunov exponents. This is done by reparametrizing Bowen balls
by contracting maps in a approach combining hyperbolic theory and Yomdin’s theory. |
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Keywords: | |
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