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Hitting time and dimension in Axiom A systems and generic interval excanges

Stefano Galatolo
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Abstract

In 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.

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Stefano Galatolo. 2005-06-24. Hitting time and dimension in Axiom A systems and generic interval excanges. https://arxiv.org/abs/math/0506516

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