Weak Gibbs measures for the natural extension of (1/β, β)-shifts

2025/09/30 by Yamashita, Miki
#28D05 #37B10 #37D35 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.25621

Abstract

In this paper we consider the weak Gibbs measures for (α, β)-shifts. In the case of α=0, Pfister and Sullivan have given a necessary and sufficient condition on β such that any equilibrium measure for a function of bounded total oscillations is a weak Gibbs measure in the natural extension of a β-shift. So it is natural to ask what happens when α>0. However, their proof cannot be applied to general (α, β)-shifts in a similar way. In this paper we consider the case of α=1/β and give a criterion for the weak Gibbs property of equilibrium measures for (1/β, β)-shifts.

Citations

• Equilibrium measures of the natural extension of beta-shifts
• Unique equilibrium states for some intermediate beta transformations
• Representations for real numbers and their ergodic properties

Related

• Equilibrium measures of the natural extension of beta-shifts
• Weak Gibbs and Equilibrium Measures for Shift Spaces
• Gibbs and equilibrium measures for some families of subshifts
• Equilibrium states which are not Gibbs measure on hereditary subshifts
• Gibbs Properties of Equilibrium States