Gibbs states for non-irreducible countable Markov shifts
Volume 221 / 2013
Fundamenta Mathematicae 221 (2013), 231-265
MSC: Primary 37B10; Secondary 37B05, 37C40, 28A80.
DOI: 10.4064/fm221-3-3
Abstract
We study Markov shifts over countable (finite or countably infinite) alphabets, i.e. shifts generated by incidence matrices. In particular, we derive necessary and sufficient conditions for the existence of a Gibbs state for a certain class of infinite Markov shifts. We further establish a characterization of the existence, uniqueness and ergodicity of invariant Gibbs states for this class of shifts. Our results generalize the well-known results for finitely irreducible Markov shifts.
