English

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 CrC^r performance function has a unique maximizing measure and the unique maximizing measure is supported on a periodic orbit, for r=1,2,,,ωr=1,2,\cdots,\infty,\omega.

Keywords

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

R2 v1 2026-06-28T21:10:29.973Z