Relative equilibrium states and class degree

2014/11/18 by Yoo, Jisang · 1 citation
#37B10 (Primary) 37D35 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1411.4880

Abstract

Given a factor code π from a shift of finite type X onto a sofic shift Y, an ergodic measure ν on Y, and a function V on X with summable variation, we prove an invariant upper bound on the number of ergodic measures on X which project to ν and maximize h(μ) + ∫ V dμ among all measures in the fiber π^-1(ν). If ν is fully supported, this bound is the class degree of π. This generalizes a previous result for the special case of V=0.

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