Abstract:

We give a method to bound the entropy of measures on SL(d,R)/SL(d,Z) which are invariant under one parameter diagonal subgroups, in terms of entropy contributions from regions of the cusp corresponding to different parabolic groups. These bounds depend on a linear functional on the Lie algebra of the Cartan group, which can then be optimized depending on the bound one is trying to obtain. We discuss how this method is utilized to obtain new sharp bounds for cusp entropies.