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\(\mathcal{C}^{2}\) surface diffeomorphisms have symbolic extensions

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We prove that \(\mathcal{C}^{2}\) 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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  1. CMLA-ENS Cachan, 61 avenue du président Wilson, 94235, Cachan Cedex, France

    David Burguet

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  1. David Burguet
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Burguet, D. \(\mathcal{C}^{2}\) surface diffeomorphisms have symbolic extensions. Invent. math. 186, 191–236 (2011). https://doi.org/10.1007/s00222-011-0317-8

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  • DOI: https://doi.org/10.1007/s00222-011-0317-8

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