Ultrametric Logarithm Laws I
arXiv:math/0506531
Abstract
We announce ultrametric analogues of the results of Kleinbock-Margulis for shrinking target properties of semisimple group actions on symmetric spaces. The main applications are S-arithmetic Diophantine approximation results and logarithm laws for buildings, generalizing the work of Hersonsky-Paulin on trees.
This announcement has been completely revised to reflect many new developments. Please direct all references to this NEW announcement. It is now co-authored work. Submitted to Discrete and Continuous Dynamical Systems