Shrinking targets for discrete time flows on hyperbolic manifolds
Dynamical Systems
2017-02-06 v1
Abstract
We prove dynamical Borel Canteli Lemmas for discrete time homogenous flows hitting a sequence of shrinking targets in a hyperbolic manifold. These results apply to both diagonalizable and unipotent flows, and any family of measurable shrinking targets. As a special case, we establish logarithm laws for the first hitting times to shrinking balls and shrinking cusp neighborhoods, refining and improving on perviously known results.
Cite
@article{arxiv.1702.01025,
title = {Shrinking targets for discrete time flows on hyperbolic manifolds},
author = {Dubi Kelmer},
journal= {arXiv preprint arXiv:1702.01025},
year = {2017}
}