Ergodic optimization for some dynamical systems beyond uniform hyperbolicity

In Ergodic optimization, one wants to find ergodic measures maximize or minimize the integral of given continuous functions. This has been succefully studied for uniformly hyperbolic systems generic functions by Bousch and Brémon. this paper, we show that several interesting beyond uniform hyperbolicity, any function a unique maximizing measure with zero entropy. some cases, also know full support. These include singular attractors, C∞ surface diffeomorphisms away from homoclinic tangencies.We try give mechanism these non-hyperbolic systems.