论文标题
标准图的最大熵度量的独特性
Uniqueness of the measure of maximal entropy for the standard map
论文作者
论文摘要
在本文中，我们证明，对于足够大的参数，标准地图具有最大熵的独特度量（M.M.M.E.）。而且，我们证明：M.M.E.是伯努利（Bernoulli），与M.M.E.我们证明了有关M.M.E. Hausdorff尺寸的一些估计。以及对歧管上测量支持的密度。对于通用大型参数，我们证明了M.M.E.的支持Hausdorff Dimension $ 2 $。我们还获得了其中几个属性的$ c^2 $ - 胡扯。
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.
