On the selection of subaction and measure for perturbed potentials

Fuente: arXiv
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Main Authors: Leplaideur, Renaud, Mengue, Jairo K
Format: Preprint
Published: 2024
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author Leplaideur, Renaud
Mengue, Jairo K
author_facet Leplaideur, Renaud
Mengue, Jairo K
contents We prove that when the Aubry set for a Lipschitz continuous potential is a subshift of finite type, then the pressure function converges exponentially fast to its asymptote as the temperature goes to 0. The speed of convergence turns out to be the unique eigenvalue for the matrix whose entries are the costs between the different irreducible pieces of the Aubry set. For a special case of Walter potential we show that pertubation of that potential that go faster to zero than the pressure do not change the selection, nor for the subaction, neither for the limit measure a zero temperature.
format Preprint
id arxiv_https___arxiv_org_abs_2404_02182
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On the selection of subaction and measure for perturbed potentials
Leplaideur, Renaud
Mengue, Jairo K
Dynamical Systems
We prove that when the Aubry set for a Lipschitz continuous potential is a subshift of finite type, then the pressure function converges exponentially fast to its asymptote as the temperature goes to 0. The speed of convergence turns out to be the unique eigenvalue for the matrix whose entries are the costs between the different irreducible pieces of the Aubry set. For a special case of Walter potential we show that pertubation of that potential that go faster to zero than the pressure do not change the selection, nor for the subaction, neither for the limit measure a zero temperature.
title On the selection of subaction and measure for perturbed potentials
topic Dynamical Systems
url https://arxiv.org/abs/2404.02182