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.

Dimension via waiting time and recurrence

GALATOLO, STEFANO
2005-01-01

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.
2005
Galatolo, Stefano
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/92171
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