English

Ergodic maximization problem for expanding maps with differentiable observables

Dynamical Systems 2021-03-23 v2

Abstract

We show that for an expanding map, the maximizing measures of a generic (open and dense) CrC^r (rNr\in\mathbb{N}) differentiable functions are supported on a single periodic orbit. [There is a gap in the discussions. For the CC^{\infty} approximation of the Lipschitz functions, we can only control the C1C^1 derivative, but we can not control the CrC^r derivatives for r2r\geq2. Elegant approximation methods might be needed to solve this problem.]

Keywords

Cite

@article{arxiv.2005.09164,
  title  = {Ergodic maximization problem for expanding maps with differentiable observables},
  author = {X. Zhang},
  journal= {arXiv preprint arXiv:2005.09164},
  year   = {2021}
}
R2 v1 2026-06-23T15:38:51.342Z