Gibbs states for non-irreducible countable Markov shifts

• Autorzy: Andrei E. Ghenciu , Mario Roy
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37C40: Smooth ergodic theory, invariant measures
• 37B10: Symbolic dynamics
• 28A80: Fractals
• 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2013
• Tom: 221
• Numer: 3
• Strony: 231-265

Daty

wydano

2013

Twórcy

autor

Andrei E. Ghenciu

• Department of Mathematics, East Central University, Ada, OK 74820, U.S.A.

autor

Mario Roy

• Department of Mathematics, Glendon College, York University, 2275 Bayview Avenue, Toronto, Canada M4N 3M6

Identyfikatory

DOI

10.4064/fm221-3-3