We show that in a rapidly mixing flow with an invariant measure, the time which is needed to hit a given section is related to a sort of conditional dimension of the measure at the section. The result is applied to the geodesic flow of compact manifolds with variable negative sectional curvature, establishing a logarithm law for such kind of flow.
Shrinking targets in fast mixing flows and the geodesic flow on negatively curved manifolds
GALATOLO, STEFANO;
2011-01-01
Abstract
We show that in a rapidly mixing flow with an invariant measure, the time which is needed to hit a given section is related to a sort of conditional dimension of the measure at the section. The result is applied to the geodesic flow of compact manifolds with variable negative sectional curvature, establishing a logarithm law for such kind of flow.File in questo prodotto:
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