2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75586In this note we prove that for equilibrium states of axiom A systems the time $τ_{B}(x)$ needed for a typical point $x$ to enter for the first time in a typical ball $B$ with radius $r$ scales as $τ_{B}(x)\sim r^{d}$ where $d$ is the local dimension of the invariant measure at the center of the ball. A similar relation is proved for a full measure set of interval excanges. Some applications to Birkoff averages of unbounded (and not $L^{1}$) functions are shown.Dynamical SystemsMathematical Physics37B20;37C45;37D20text