2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73549For measure preserving dynamical systems on metric spaces we study the time needed by a typical orbit to return back close to its starting point. We prove that when the decay of correlation is super-polynomial the recurrence rates and the pointwise dimensions are equal. This gives a broad class of systems for which the recurrence rate equals the Hausdorff dimension of the invariant measure.Dynamical Systems37B20, 37C45, 37A25text