Ergodic optimization for some dynamical systems beyond uniform hyperbolicity

In Ergodic optimization, one wants to find ergodic measures to maximize or minimize the integral of given continuous functions. This has been succefully studied for uniformly hyperbolic systems for generic continuous functions by Bousch and Brémon. 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 include singular hyperbolic attractors, (Formula presented.) surface diffeomorphisms and diffeomorphisms away from homoclinic tangencies.We try to give a uniform mechanism for these non-hyperbolic systems.