Lyapunov optimizing measures and periodic measures for C² expanding maps

2021/04/09 by Huang, Wen, Xu, Leiye, Yang, Dawei
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.04213

Abstract

We prove that there exists an open and dense subset U in the space of C² expanding self-maps of the circle \mathbbT such that the Lyapunov minimizing measures of any T∈\mathcal U are uniquely supported on a periodic orbit.This answers a conjecture of Jenkinson-Morris in the C² topology.

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