Lyapunov optimizing measures and periodic measures for $C^2$ expanding maps

Wen Huang; Leiye Xu; Dawei Yang

Lyapunov optimizing measures and periodic measures for $C^2$ expanding maps

Dynamical Systems 2021-04-12 v1

Authors: Wen Huang , Leiye Xu , Dawei Yang

Abstract

We prove that there exists an open and dense subset $\mathcal{U}$ in the space of $C^{2}$ expanding self-maps of the circle $\mathbb{T}$ such that the Lyapunov minimizing measures of any $T\in{\mathcal U}$ are uniquely supported on a periodic orbit.This answers a conjecture of Jenkinson-Morris in the $C^2$ topology.

Keywords

Lyapunov minimizing measures periodic orbits C^2 expanding maps circle maps open dense subset

Cite

@article{arxiv.2104.04213,
  title  = {Lyapunov optimizing measures and periodic measures for $C^2$ expanding maps},
  author = {Wen Huang and Leiye Xu and Dawei Yang},
  journal= {arXiv preprint arXiv:2104.04213},
  year   = {2021}
}

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