Ergodic measures of intermediate entropies for dynamical systems with the approximate product property

Abstract

For a dynamical system satisfying the approximate product property and asymptotically entropy expansiveness, we characterize a delicate structure of the space of invariant measures: The ergodic measures of intermediate entropies and the ones of intermediate pressures are generic in certain subspaces. Consequently, the conjecture of Katok that ergodic measures of arbitrary intermediate entropy exist is verified for a broad class of systems.