Equilibrium states by synchronization, symbolic extensions, and factors

We combine the two classical topological concepts, time-preserving topological factors and synchronizing time-changes of a continuous flow, and explore some of their thermodynamic consequences. Particular focus is put on equilibrium states and, in particular, measures of maximal entropy, with emphasis on geodesic flows on rank-one surfaces of nonpositive curvature and their time-preserving expansive topological factors for which we investigate the scaled geometric potentials.