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

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

2007-08-02

arxiv.org/abs/0708.0379v3

Stoch. Dyn. 9 (2009) 81-100

Mathematics

Dynamical Systems

Proof of Proposition 5 simplified

Scientific paper

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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