Logarithm Laws for Unipotent Flows, II
  We prove analogs of the logarithm laws of Sullivan and Kleinbock-Margulis in the context of unipotent flows. In particular, we prove results for horospherical actions on homogeneous spaces $G/\Gamma$. We describe some relations with multi-dimensional diophantine approximation. 
Jayadev S. Athreya and Gregory Margulis
math.DS