Ergodic optimization for some dynamical systems beyond uniform hyperbolicity

Abstract

In this paper, we show that for several interesting systems beyond uniform hyperbolicity, any generic continuous function has a unique maximizing measure with zero entropy. In some cases, we also know that the maximizing measure has full support. These interesting systems including singular hyperbolic attractors, $C^{\infty }$ surface diffeomorphisms and diffeomorphisms away from homoclinic tangencies.