Typicality of periodic optimization over an expanding circle map
Dynamical Systems
2025-02-18 v2
Abstract
We study the ergodic optimization problem over a real analytic expanding circle map. We show that in both the topological and the measure-theoretical senses, a typical performance function has a unique maximizing measure and the unique maximizing measure is supported on a periodic orbit, for .
Cite
@article{arxiv.2501.10949,
title = {Typicality of periodic optimization over an expanding circle map},
author = {Rui Gao and Weixiao Shen and Ruiqin Zhang},
journal= {arXiv preprint arXiv:2501.10949},
year = {2025}
}
Comments
26 pages, minor corrections in section 5