TY - JOUR

T1 - Gibbs and equilibrium measures for some families of subshifts

AU - Meyerovitch, Tom

PY - 2013/6/1

Y1 - 2013/6/1

N2 - For subshifts of finite typeÂ (SFTs), any equilibrium measure is Gibbs, as long as f has d-summable variation. This is a theorem of Lanford and Ruelle. Conversely, a theorem of Dobrušin states that for strongly irreducible subshifts, shift-invariant Gibbs measures are equilibrium measures. Here we prove a generalization of the Lanford-Ruelle theorem: for all subshifts, any equilibrium measure for a function with d-summable variation is 'topologically Gibbs'. This is a relaxed notion which coincides with the usual notion of a Gibbs measure for SFTs. In the second part of the paper, we study Gibbs and equilibrium measures for some interesting families of subshifts: β-shifts, Dyck shifts and Kalikow-type shifts (defined below). In all of these cases, a Lanford-Ruelle-type theorem holds. For each of these families, we provide a specific proof of the result.

AB - For subshifts of finite typeÂ (SFTs), any equilibrium measure is Gibbs, as long as f has d-summable variation. This is a theorem of Lanford and Ruelle. Conversely, a theorem of Dobrušin states that for strongly irreducible subshifts, shift-invariant Gibbs measures are equilibrium measures. Here we prove a generalization of the Lanford-Ruelle theorem: for all subshifts, any equilibrium measure for a function with d-summable variation is 'topologically Gibbs'. This is a relaxed notion which coincides with the usual notion of a Gibbs measure for SFTs. In the second part of the paper, we study Gibbs and equilibrium measures for some interesting families of subshifts: β-shifts, Dyck shifts and Kalikow-type shifts (defined below). In all of these cases, a Lanford-Ruelle-type theorem holds. For each of these families, we provide a specific proof of the result.

UR - http://www.scopus.com/inward/record.url?scp=84879861456&partnerID=8YFLogxK

U2 - 10.1017/S0143385712000053

DO - 10.1017/S0143385712000053

M3 - Article

AN - SCOPUS:84879861456

VL - 33

SP - 934

EP - 953

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

IS - 3

ER -