Shrinking Targets for Semisimple Groups

TL;DR

This paper investigates how semisimple groups acting on homogeneous spaces approach shrinking targets, with implications for logarithm laws and Diophantine approximation, advancing understanding of dynamical systems and number theory.

Contribution

It introduces new results on shrinking target problems for semisimple group actions, connecting dynamical behavior with Diophantine approximation.

Findings

Established logarithm laws for semisimple group actions

Linked shrinking target phenomena to Diophantine approximation

Provided new bounds on hitting times for orbits

Abstract

We study the shrinking target problem for actions of semisimple groups on homogeneous spaces, with applications to logarithm laws and Diophantine approximation.