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Exponential Decay of Correlations for Piecewise Cone Hyperbolic Contact Flows

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Abstract

We prove exponential decay of correlations for a realistic model of piecewise hyperbolic flows preserving a contact form, in dimension three. This is the first time exponential decay of correlations is proved for continuous-time dynamics with singularities on a manifold. Our proof combines the second author’s version (Liverani in Ann Math 159:1275–1312, 2004) of Dolgopyat’s estimates for contact flows and the first author’s work with Gouëzel (J Mod Dyn 4:91–137, 2010) on piecewise hyperbolic discrete-time dynamics.

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Correspondence to Viviane Baladi.

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Communicated by G. Gallavotti

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Baladi, V., Liverani, C. Exponential Decay of Correlations for Piecewise Cone Hyperbolic Contact Flows. Commun. Math. Phys. 314, 689–773 (2012). https://doi.org/10.1007/s00220-012-1538-4

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