Rapid decay of correlations for nonuniformly hyperbolic flows

Melbourne, Ian

doi:10.1090/S0002-9947-06-04267-X

Rapid decay of correlations for nonuniformly hyperbolic flows
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by Ian Melbourne PDF

Trans. Amer. Math. Soc. 359 (2007), 2421-2441 Request permission

Abstract:

We show that superpolynomial decay of correlations (rapid mixing) is prevalent for a class of nonuniformly hyperbolic flows. These flows are the continuous time analogue of the class of nonuniformly hyperbolic maps for which Young proved exponential decay of correlations. The proof combines techniques of Dolgopyat and operator renewal theory. It follows from our results that planar periodic Lorentz flows with finite horizons and flows near homoclinic tangencies are typically rapid mixing.

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