Open Zooming Systems: Uniqueness of Equilibrium States

Abstract

We study open zooming systems and potentials with uniqueness of equilibrium states. The uniqueness is established for a certain class of zooming potentials when the map is topologically exact, including the null one. Also, with equilibrium stability, we prove that there exists a countable and an open sets of continuous potentials with uniqueness which are both dense in the set of continuous potentials with finiteness. The results here are related to the works [14] and [49] where finiteness and stability are studied.

arXiv commentWe have generalized the nonuniformly expanding maps and hyperbolic potentials to zooming context. By using results of the same authors, we give another proof of uniqueness claimed for Viana maps and now for other zooming systems. arXiv admin note: substantial text overlap with arXiv:2010.08143