Low complexity of optimizing measures over an expanding circle map

Autor:	Gao, Rui, Shen, Weixiao
Rok vydání:	2022
Předmět:	Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	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. Comment: 15 pages, minor corrections
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2206.05467 Zobrazit plný text záznamu View this record from Arxiv