Hitting time and dimension in Axiom A systems and generic interval excanges
نویسنده
چکیده
In this note we prove that for equilibrium states of axiom A systems the time τB(x) needed for a typical point x to enter for the first time in a typical ball B with radius r scales as τB(x) ∼ 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 ) functions are shown.
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