Exponential decay of correlations for piecewise cone hyperbolic contact flows

Details Exponential decay of correlations for piecewise cone hyperbolic contact flows Exponential decay of correlations for piecewise cone hyperbolic contact flows

2011-05-03

arxiv.org/abs/1105.0567v2

Mathematics

Dynamical Systems

76 pages, 4 figures included in LaTeX file

Scientific paper

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 of Dolgopyat's estimates for contact flows and the first author's work with Gou\"ezel on piecewise hyperbolic discrete-time dynamics. (Presentation revised.)

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