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Exchangeable, Gibbs and equilibrium measures for Markov subshifts

Published online by Cambridge University Press:  12 February 2007

J. AARONSON  and
H. NAKADA
J. AARONSON
Affiliation:
School of Mathematical Sciences, Tel Aviv University, 69978 Tel Aviv, Israel (e-mail: aaro@tau.ac.il)
H. NAKADA
Affiliation:
Department of Mathematics, Keio University, Hiyoshi 3-14-1 Kohoku, Yokohama 223, Japan (e-mail: nakada@math.keio.ac.jp)
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Abstract

We study a class of strongly irreducible, multidimensional, topological Markov shifts, comparing two notions of ‘symmetric measure’: exchangeability and the Gibbs (or conformal) property. We show that equilibrium measures for such shifts (unique and weak Bernoulli in the one-dimensional case) exhibit a variety of spectral properties.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 2 , April 2007 , pp. 321 - 339
Copyright
2007 Cambridge University Press

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