English

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 Γ\G\Gamma\backslash G with GG a semisimple group and Γ\Gamma 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.

Keywords

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

R2 v1 2026-06-22T21:27:08.226Z