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Return time statistics for unimodal maps. (English) Zbl 1082.37037
Summary: We prove that a non-flat S-unimodal map satisfying a weak summability condition has exponential return time statistics on intervals around a.e. point. Moreover we prove that the convergence to the entropy in the Ornstein-Weiss formula enjoys normal fluctuations.

MSC:
37E05 Dynamical systems involving maps of the interval
37B20 Notions of recurrence and recurrent behavior in topological dynamical systems
37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37A05 Dynamical aspects of measure-preserving transformations
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