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

中文翻译：

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标准图的最大熵测度的唯一性

在本文中，我们证明了对于足够大的参数，标准图具有唯一的最大熵（mme）度量。此外，我们证明：mme是伯努利，并且具有Lyapunov指数的周期点相对于mme远离零等分分布我们证明了有关mme的Hausdorff尺寸以及流形上度量支持的密度的一些估计。对于一个通用的大参数，我们证明了mme的支持具有Hausdorff维数2。我们还获得了其中一些特性的$ C ^ 2 $-鲁棒性。