Shrinking targets for discrete time flows on hyperbolic manifolds

2017/02/03 by Dubi Kelmer, Kelmer, Dubi
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1702.01025

openalex publication_date 2017/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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