Geodesic
Gibbs states for non-irreducible countable Markov shifts
Andrei E. Ghenciu 1   ; Mario Roy 2
1 Department of Mathematics East Central University Ada, OK 74820, U.S.A.
2 Department of Mathematics Glendon College York University 2275 Bayview Avenue Toronto, Canada M4N 3M6
Fundamenta Mathematicae, Tome 221 (2013) no. 3, pp. 231-265 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm221-3-3
Keywords: study markov shifts countable finite countably infinite alphabets shifts generated incidence matrices particular derive necessary sufficient conditions existence gibbs state certain class infinite markov shifts further establish characterization existence uniqueness ergodicity invariant gibbs states class shifts results generalize well known results finitely irreducible markov shifts

Andrei E. Ghenciu  1   ; Mario Roy  2

1 Department of Mathematics East Central University Ada, OK 74820, U.S.A.
2 Department of Mathematics Glendon College York University 2275 Bayview Avenue Toronto, Canada M4N 3M6 
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Andrei E. Ghenciu; Mario Roy. Gibbs states for non-irreducible countable Markov shifts. Fundamenta Mathematicae, Tome 221 (2013) no. 3, pp. 231-265. doi: 10.4064/fm221-3-3

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