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Dimension via Waiting time and Recurrence

S. Galatolo
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Abstract

Quantitative recurrence indicators are defined by measuring the first entrance time of the orbit of a point $x$ in a decreasing sequence of neighborhoods of another point $y$. It is proved that these recurrence indicators are a.e. greater or equal to the local dimension at $y$, then these recurrence indicators can be used to have a numerical upper bound on the local dimension of an invariant measure.

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S. Galatolo. 2003-10-01. Dimension via Waiting time and Recurrence. https://arxiv.org/abs/math/0309223

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