Shrinking targets problems for flows on homogeneous spaces
Dynamical Systems
2020-06-09 v2
Abstract
We study shrinking targets problems for discrete time flows on a homogenous space with a semisimple group and an irreducible lattice. Our results apply to both diagonalizable and unipotent flows, and apply to very general families of shrinking targets. As a special case, we establish logarithm laws for cusp excursions of unipotent flows answering a question of Athreya and Margulis.
Cite
@article{arxiv.1708.08953,
title = {Shrinking targets problems for flows on homogeneous spaces},
author = {Dubi Kelmer and Shucheng Yu},
journal= {arXiv preprint arXiv:1708.08953},
year = {2020}
}
Comments
31 pages; Corollary 1.2 is now proved in full generality; removed the assumption that $\{\mu(B_m)\}$ is non-increasing in Proposition 5.4; typos corrected