Return time statistics for invariant measures for interval maps with positive Lyapunov exponent
Abstract
Description
We prove that multimodal maps with an absolutely continuous invariant measure have exponential return time statistics around a.e. point. We also show a `polynomial Gibbs property' for these systems, and that the convergence to the entropy in the Ornstein-Weiss formula has normal fluctuations. These results are also proved for equilibrium states of some Hoelder potentials.
Proof of Proposition 5 simplified
Proof of Proposition 5 simplified