Uniqueness of the measure of maximal entropy for the standard map

  • Davi Obata

    University of Chicago, USA
Uniqueness of the measure of maximal entropy for the standard map cover

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Abstract

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 -robustness of several of these properties.

Cite this article

Davi Obata, Uniqueness of the measure of maximal entropy for the standard map. Comment. Math. Helv. 96 (2021), no. 1, pp. 79–111

DOI 10.4171/CMH/508