On density of infinite subsets II: Dynamics on homogeneous spaces
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Abstract:
Let $G$ be a noncompact semisimple Lie group, let $\Gamma$ be an irreducible cocompact lattice in $G$, and let $P<G$ be a minimal parabolic subgroup. We consider the dynamics of $P$ acting on $G/\Gamma$ by left translation. For any infinite subset $A\subset G/\Gamma$, we show that, for any $\epsilon >0$, there is a $g\in P$ such that $gA$ is $\epsilon$-dense. We also prove a similar result for certain discrete group actions on $\mathbb T^n$.References
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Additional Information
- Changguang Dong
- Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
- Address at time of publication: Department of Mathematics, University of Maryland, College Park, Maryland 20742
- MR Author ID: 1209956
- Email: dongchangguang@gmail.com
- Received by editor(s): November 12, 2017
- Received by editor(s) in revised form: June 6, 2018
- Published electronically: November 5, 2018
- Additional Notes: This work was partially supported by NSF grant #1602409.
- Communicated by: Nimish Shah
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 751-761
- MSC (2010): Primary 37C85, 22F30
- DOI: https://doi.org/10.1090/proc/14298
- MathSciNet review: 3894913