Weak Gibbs measures for the natural extension of (κ/β, β)-shifts
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 [Pfister and Sullivan, Equilibrium measures of the natural extension of β-shifts, Ergod. Theo. & Dyn. Syst. 42 (2022), pp. 2415–2430]. 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=κ/β and give a criterion for the weak Gibbs property of equilibrium measures for (κ/β,β)-shifts.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Complex Systems and Time Series Analysis
Stochastic processes and financial applications
Publication details
- Journal / source
- Dynamical Systems
- Publisher
- Informa UK Limited
- Volume
- 41
- Issue
- 3
- Pages
- 390–415
- Publication date
- 4 May 2026
- Language
- EN