On the selection of subaction and measure for perturbed potentials

À propos de la sélection de subactions et de mesures à température zéro

Renaud Leplaideur (1, 2) , Jairo K Mengue (3)

1 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique
2 ISEA - Institut de sciences exactes et appliquées
3 UFRGS - Departamento de Matemática Pura e Aplicada [Porto Alegre]

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.

Keywords: Ergodic optimization; selection; zero temperature

Domains: Dynamical Systems [math.DS]

Renaud Leplaideur, Jairo K Mengue. On the selection of subaction and measure for perturbed potentials. 2024. ⟨hal-04528280⟩