Abstract:
Recently, Einsiedler and the authors provided a bound in terms of escape of mass for the amount by which upper-semicontinuity for metric entropy fails for diagonal
ows on homogeneous spaces nG, where G is any connected semisimple Lie group of real rank 1 with nite center, and is any nonuniform lattice in G. We show that this bound is sharp, and apply the methods used to establish bounds for the Hausdorff dimension of the set of points which diverge on average.