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On calibrated and separating sub-actions

On calibrated and separating sub-actions We consider a one-sided transitive subshift of finite type σ: Σ → Σ and a Hölder observable A. In the ergodic optimization model, one is interested in properties of A-minimizing probability measures. If Ā denotes the minimizing ergodic value of A, a sub-action u for A is by definition a continuous function such that A ≥ u ○ σ − u + Ā. We call contact locus of u with respect to A the subset of Σ where A = u ○ σ − u + Ā. A calibrated sub-action u gives the possibility to construct, for any point x ε Σ, backward orbits in the contact locus of u. In the opposite direction, a separating sub-action gives the smallest contact locus of A, that we call Ω(A), the set of non-wandering points with respect to A. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

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References (24)

Publisher
Springer Journals
Copyright
Copyright © 2009 by Springer
Subject
Mathematics; Theoretical, Mathematical and Computational Physics; Mathematics, general
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s00574-009-0028-6
Publisher site
See Article on Publisher Site

Abstract

We consider a one-sided transitive subshift of finite type σ: Σ → Σ and a Hölder observable A. In the ergodic optimization model, one is interested in properties of A-minimizing probability measures. If Ā denotes the minimizing ergodic value of A, a sub-action u for A is by definition a continuous function such that A ≥ u ○ σ − u + Ā. We call contact locus of u with respect to A the subset of Σ where A = u ○ σ − u + Ā. A calibrated sub-action u gives the possibility to construct, for any point x ε Σ, backward orbits in the contact locus of u. In the opposite direction, a separating sub-action gives the smallest contact locus of A, that we call Ω(A), the set of non-wandering points with respect to A.

Journal

Bulletin of the Brazilian Mathematical Society, New SeriesSpringer Journals

Published: Nov 10, 2009

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