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arXiv · 1702.01025

Shrinking targets for discrete time flows on hyperbolic manifolds

Dubi Kelmer
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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.

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Dubi Kelmer. 2017-02-03. Shrinking targets for discrete time flows on hyperbolic manifolds. https://arxiv.org/abs/1702.01025

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