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Uniqueness of equilibrium measures for countable Markov shifts and multidimensional piecewise expanding maps

Published online by Cambridge University Press:  23 September 2003

JÉRÔME BUZZI  and
OMRI SARIG
JÉRÔME BUZZI
Affiliation:
CMAT, U.M.R. 7640 du C.N.R.S., Ecole Polytechnique, 91128 Palaiseau Cedex, France (e-mail: [email protected])
OMRI SARIG
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK (e-mail: [email protected])
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Abstract

We prove that potentials with summable variations on topologically transitive countable Markov shifts have at most one equilibrium measure. We apply this to multidimensional piecewise expanding maps using their Markov diagrams.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 5 , October 2003 , pp. 1383 - 1400
Copyright
2003 Cambridge University Press

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