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arXiv · 1101.0486

Shrinking targets in fast mixing flows and the geodesic flow on negatively curved manifolds

Stefano Galatolo·Isaia Nisoli
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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 variable negative sectional curvature manifolds, establishing a logarithm law for such kind of flow.

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Stefano Galatolo, Isaia Nisoli. 2011-01-15. Shrinking targets in fast mixing flows and the geodesic flow on negatively curved manifolds. https://doi.org/10.1088/0951-7715%2F24%2F11%2F005

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