Equilibrium states by synchronization, symbolic extensions, and factors

We study two classical topological concepts, time-preserving topological factors and synchronizing time-changes of a continuous flow, and explore their thermodynamic consequences. Special focus is on equilibrium states and, in particular, measures of maximal entropy. We combine these approaches with symbolic extensions in the setting of geodesic flows. As the main application, we show the uniqueness of equilibrium states for the scaled geometric potentials of geodesic flows on closed surfaces without focal points.