2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78398For non uniformly hyperbolic maps of the interval with exponential decay of correlations we prove that the law of closest return to a given point when suitably normalized is almost surely asymptotically exponential. A similar result holds when the reference point is the initial point of the trajectory. We use the framework for non uniformly hyperbolic dynamical systems developed by L.S.Young.Dynamical Systems34C35, 60G70text