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

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

2005-06-24

arxiv.org/abs/math/0506516v1

Mathematics

Dynamical Systems

Scientific paper

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.

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