S. Galatolo
Published 2003-09-13, updated 2003-10-01Version 2
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.
Comments: This replace the previous version. New recent references are added
Local dimensions for the random beta-transformation
On the dimension of invariant measures of endomorphisms of $\mathbb{CP}^k$
Dimension and waiting time in rapidly mixing systems
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