Shrinking targets in fast mixing flows and the geodesic flow on negatively curved manifolds
Dynamical Systems
2011-10-20 v2
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.
Keywords
Cite
@article{arxiv.1101.0486,
title = {Shrinking targets in fast mixing flows and the geodesic flow on negatively curved manifolds},
author = {Stefano Galatolo and Isaia Nisoli},
journal= {arXiv preprint arXiv:1101.0486},
year = {2011}
}
Comments
15 pages