Criterion for Finiteness of BMS Measure

In many useful settings, having a finite BMS measure on a flow space allows people to normalize the BMS measure into a probability measure and facilitates powerful ergodic theoretic tools. This often leads to asymptotic estimates for counting orbital points and establishing equidistribution results. Hence, it is important to know when a dynamical system admits a finite BMS measure. In this talk, I will introduce the criterion for the finiteness of BMS measure on the unit tangent bundle of a negatively curved manifold introduced by Pit-Schapira. If time permits, I will also present my recent work that extends this criterion to the setting of discrete subgroups of higher rank semisimple Lie groups.