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Existence uniqueness and ratio decomposition for Gibbs states via duality

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Pinto, A. A. and Rand, D. A. (David A.). (2001) Existence uniqueness and ratio decomposition for Gibbs states via duality. Ergodic Theory and Dynamical Systems, Vol.21 (No.2). pp. 533-543. ISSN 0143-3857

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Official URL: http://dx.doi.org/10.1017/S0143385701001262

Abstract

We give an elementary proof of existence and uniqueness of Gibbs states for Hölder weight systems on subshifts of finite type. This uses a notion of duality for such subshifts. The approach of Paterson [2] is used to construct a measure with a prescribed Jacobian and the duality is used to produce an invariant measure from this.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Probabilities, Probabilistic number theory, Stochastic processes, Jacobians, Functions of several complex variables
Journal or Publication Title:	Ergodic Theory and Dynamical Systems
Publisher:	Cambridge University Press
ISSN:	0143-3857
Date:	April 2001
Volume:	Vol.21
Number:	No.2
Page Range:	pp. 533-543
Identification Number:	10.1017/S0143385701001262
Status:	Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Fundação Calouste Gulbenkian (FCG), Fundação para a Ciência e a Tecnologia (FCT), PRAXIS (Organization), European Science Foundation (ESF), Universidade do Porto. Centro de Matemática Aplicada (CMA), Science and Engineering Research Council (Great Britain) (SERC), European Union (EU)
References:	[1] R. Bowen. Equilibrium States and the Ergodic Theory of Axiom A Diffeomorphisms (Lecture Notes in Mathematics, 470). Springer, New York, 1975. [2] S. J. Paterson. The limit set of a Fuchsian group. Acta. Math. 136 (1976), 241–273. [3] A. A. Pinto and D. A. Rand. Geometric measures for hyperbolic surface dynamics. Preprint, 1999. [4] D. Sullivan. Conformal Dynamical Systems (Springer Lecture Notes in Mathematics, 1007). Springer, New York, 1983, pp. 725–752.
URI:	http://wrap.warwick.ac.uk/id/eprint/820