Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc.

Online first article July 11, 2024

Copyright © The Korean Mathematical Society.

A necessary and sufficient condition for the existence of invariant Gibbs measures

Minkyu Kim

Ajou University

Abstract

In this paper, we study a relation between the existence of invariant Gibbs measures and the balanced property of subshifts. We show that a subshift $X$ has an invariant Gibbs measure for $f\in C\left(X,\mathbb{R}\right)$ if and only if it is balanced with respect to $f$.

Keywords: symbolic dynamics, subshifts, Gibbs measures, balanced property

MSC numbers: 37B10

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