Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors

Details Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors

2012-04-03

arxiv.org/abs/1204.0703v1

Mathematics

Dynamical Systems

36 pages; 03 figures

Scientific paper

We consider two dimensional maps preserving a foliation which is uniformly contracting and a one dimensional associated quotient map having exponential convergence to equilibrium (iterates of Lebesgue measure converge exponentially fast to physical measure). We prove that these maps have exponential decay of correlations over a large class of observables. We use this result to deduce exponential decay of correlations for the Poincare maps of a large class of singular hyperbolic flows. From this we deduce logarithm laws for these flows.

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