Georgia Institute of Technology College of Sciences

In this talk, we will discuss recent progress in the theory of smooth star flows that contain singularities and consider their expansiveness, continuity of the topological pressure, and the existence and uniqueness of equilibrium states. We will prove an ergodic version of the Spectral Decomposition Conjecture: $C^1$ open and densely, every singular star flow has only finitely many ergodic measures of maximal entropy, and only finitely many ergodic equilibrium states for Holder continuous potentials satisfying a mild yet optimal condition. Joint with M.J. Pacifico and J. Yang.