Gibbs and equilibrium measures for some families of subshifts
| dc.creator | Meyerovitch, Tom | |
| dc.date | 2009-03-08 | |
| dc.date.accessioned | 2026-07-07T12:50:22Z | |
| dc.date.available | 2026-07-07T12:50:22Z | |
| dc.description | For SFTs, any equilibrium measure is Gibbs, as long a $f$ has $d$-summable variation. This is a theorem of Lanford and Ruelle. Conversely, a theorem of Dobru{š}in 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. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/0903.1426 | |
| dc.identifier | http://arxiv.org/abs/0903.1426 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222664 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Mathematical Physics | |
| dc.subject | 37B10; 37D35 | |
| dc.title | Gibbs and equilibrium measures for some families of subshifts | |
| dc.type | text |