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

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

2011-01-03

arxiv.org/abs/1101.0486v2

Mathematics

Dynamical Systems

15 pages

Scientific paper

10.1088/0951-7715/24/11/005

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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