An avoidance principle and Margulis functions for expanding translates of unipotent orbits. (English) Zbl 07924659
Summary: We prove an avoidance principle for expanding translates of unipotent orbits for some quotients of semisimple Lie groups. In addition, we prove a quantitative isolation result of closed orbits and give an upper bound on the number of closed orbits of bounded volume. The proofs of our results rely on the construction of a Margulis function and the theory of finite dimensional representations of semisimple Lie groups.
MSC:
| 22F30 | Homogeneous spaces |
| 37D40 | Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) |
| 22E46 | Semisimple Lie groups and their representations |
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