arXiv:2007.05862 Abstract | arXiv Analytics

arXiv:2007.05862 [math.DS]Abstract References Reviews Resources

A Dobrushin-Lanford-Ruelle theorem for irreducible sofic shifts

Published 2020-07-11Version 1

We show that for a potential with summable variations on an irreducible sofic shift in one dimension, the equilibrium measures are precisely the shift-invariant Gibbs measures. The main tool in the proof is a preservation of Gibbsianness result for almost invertible factor codes on irreducible shifts of finite type, which we then extend to finite-to-one codes by applying the results about equilibrium measures.

Comments: 14 pages, 1 diagram

Categories: math.DS

Subjects: 37D35, 37B10

Keywords: irreducible sofic shift, dobrushin-lanford-ruelle theorem, equilibrium measures, shift-invariant gibbs measures, invertible factor codes

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