Decay Of Correlations For Maps Research Articles

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

Erratum to: 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

We consider 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 suitable Poincaré maps of a large class of singular hyperbolic flows. From this we deduce a logarithm law for these flows.

Subexponential decay of correlations

We describe a method for proving subexponential lower bounds for correlations functions, and apply it to study decay of correlations for maps with countable Markov partitions. One result is that LS Young’s upper estimates [Y2] are optimal in many situations. Our method is based on a general result concerning the asymptotics of renewal sequences of bounded operators acting on Banach spaces, which we apply to the iterates of the transfer operator.

Statistical Properties of Maps¶with Indifferent Periodic Points

In this note we present an axiomatic approach to the decay of correlations for maps of arbitrary dimension with indifferent periodic points. As applications, we apply our results to the well-known Manneville–Pomeau equation and the inhomogeneous diophantine approximation algorithm.