2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/227476We 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 simplifiedDynamical Systems37E05, 37A05, 37B20, 37D25text