A shrinking target problem with target at infinity in rank one homogeneous spaces (Q2003538)

The author considers the shrinking target problem with target at infinity in the homogeneous space \(G/\Gamma\), where \(G\) is a simple Lie group of real rank one and \(\Gamma\) is a nonuniform lattice in \(G\). The author studies the subset of points whose trajectories under a semisimple flow on \(G/\Gamma\) enter into cusps infinitely often with certain rate. The main results are an explicit formula for the Hausdorff dimension of such a subset and a Jarník-Besicovitch theorem on Diophantine approximation in Heisenberg groups.