Low complexity of optimizing measures over an expanding circle map
Dynamical Systems
2022-08-01 v2
Abstract
In this paper, we prove that for real analytic expanding circle maps, all optimizing measures of a real analytic potential function have zero entropy, unless the potential is cohomologous to constant. We use the group structure of the symbolic space to solve a transversality problem involved. We also discuss applications to optimizing measures for generic smooth potentials and to Lyapunov optimizing measures.
Keywords
Cite
@article{arxiv.2206.05467,
title = {Low complexity of optimizing measures over an expanding circle map},
author = {Rui Gao and Weixiao Shen},
journal= {arXiv preprint arXiv:2206.05467},
year = {2022}
}
Comments
15 pages, minor corrections