Shrinking targets problems for flows on homogeneous spaces
Abstract
We study shrinking targets problems for discrete time flows on a homogenous space $\Gamma\backslash G$ with $G$ a semisimple group and $\Gamma$ 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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2017
- DOI:
- 10.48550/arXiv.1708.08953
- arXiv:
- arXiv:1708.08953
- Bibcode:
- 2017arXiv170808953K
- Keywords:
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- Mathematics - Dynamical Systems
- E-Print:
- 31 pages