Uniqueness of the measure of maximal entropy for the standard map

In this paper we prove that for sufficiently large parameters the standard map has a unique measure of maximal entropy (m.m.e.). Moreover, prove: m.m.e. is Bernoulli, and periodic points with Lyapunov exponents bounded away from zero equidistribute respect to m.m.e.We some estimates regarding Hausdorff dimension about density support on manifold. For generic parameter, 2. We also obtain $C^2$-robustness several these properties.