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