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We prove that multimodal maps with an absolutely continuous invariant measurehave exponential return time statistics around a.e. point. We also show a`polynomial Gibbs property' for these systems, and that the convergence to theentropy in the Ornstein-Weiss formula has normal fluctuations. These resultsare also proved for equilibrium states of some Hoelder potentials.

RETURN TIME STATISTICS OF INVARIANT MEASURES FOR INTERVAL MAPS WITH POSITIVE LYAPUNOV EXPONENT