Dimension via Waiting time and Recurrence

By Stefano Galatolo. 2003

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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.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/13c6512dc9de539aaea7b7c9075e92af4bdfdb8a