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Type: Artigo de periódico
Title: On calibrated and separating sub-actions
Author: Garibaldi, E
Lopes, AO
Thieullen, P
Abstract: We consider a one-sided transitive subshift of finite type sigma : Sigma -> Sigma and a Holder observable A. In the ergodic optimization model, one is interested in properties of A-minimizing probability measures. If (A) over bar denotes the minimizing ergodic value of A, a sub-action u for A is by definition a continuous function such that A >= u o sigma - u + (A) over bar. We call contact locus of u with respect to A the subset of Sigma where A = u o sigma - u + (A) over bar. A calibrated sub-action u gives the possibility to construct, for any point x is an element of Sigma, 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 Omega (A), the set of non-wandering points with respect to A. We prove that separating sub-actions are generic among Holder sub-actions. We also prove that, under certain conditions on Omega(A), any calibrated sub- action is of the form u(x) = u(x(i)) + h(A)(x(i), x) for some x(i) is an element of Omega (A), where h(A)(x, y) denotes the Peierls barrier of A. We present the proofs in the holonomic optimization model, a formalism which allows to take into account a two-sided transitive subshift of finite type ((Sigma) over cap, (sigma) over cap).
Subject: ergodic optimization
minimizing measures
separating sub-actions
Peierls barrier
Country: EUA
Editor: Springer
Citation: Bulletin Of The Brazilian Mathematical Society. Springer, v. 40, n. 4, n. 577, n. 602, 2009.
Rights: fechado
Date Issue: 2009
Appears in Collections:Unicamp - Artigos e Outros Documentos

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