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arXiv · 2104.04213

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

Wen Huang·Leiye Xu·Dawei Yang
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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.

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Wen Huang, Leiye Xu, Dawei Yang. 2021-04-09. Lyapunov optimizing measures and periodic measures for $C^2$ expanding maps. https://arxiv.org/abs/2104.04213

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