In this note we prove that for equilibrium states of axiom A systems the time $\tau_{ B}(x)$ needed for a typical point $x$ to enter for the first time in a typical ball $B$ with radius $r$ scales as $\tau_{ B}(x)\sim r^{ d}$ 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.
Categories: math.DS math-ph math.MP