An avoidance principle and Margulis functions for expanding translates of unipotent orbits

Abstract: Avoidance principles — quantifying how much time trajectories avoid certain subsets of the ambient space — have been fruitful in the study of dynamical systems. We prove an avoidance principle for expanding translates of unipotent orbits for some semisimple homogeneous spaces. 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 proof of our results relies on the construction of a Margulis function and the theory of finite dimensional representations of semisimple Lie groups. This is joint work with Anthony Sanchez.

dynamical systemsnumber theory

Audience: general audience

New England Dynamics and Number Theory Seminar