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Existence, uniqueness and ratio decomposition for Gibbs states via duality

Published online by Cambridge University Press:  30 March 2001

A. A. PINTO  and
D. A. RAND
A. A. PINTO
Affiliation:
Departamento de Matemática Aplicada, Faculdade de Ciências, Universidade do Porto, 4000 Porto, Portugal (e-mail: [email protected])
D. A. RAND
Affiliation:
Nonlinear Systems Laboratory, Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK (e-mail: [email protected])
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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

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 2 , April 2001 , pp. 533 - 543
Copyright
2001 Cambridge University Press

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