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arXiv · 0708.0379

Return time statistics for invariant measures for interval maps with positive Lyapunov exponent

Henk Bruin·Mike Todd
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Abstract

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.

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Henk Bruin, Mike Todd. 2009-04-20. Return time statistics for invariant measures for interval maps with positive Lyapunov exponent. https://arxiv.org/abs/0708.0379

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