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On the selection of subaction and measure for perturbed potentials

Part of: Dynamical systems with hyperbolic behavior Ergodic theory

Published online by Cambridge University Press:  17 December 2025

RENAUD LEPLAIDEUR Open the ORCID record for RENAUD LEPLAIDEUR [Opens in a new window]  and
JAIRO KRÁS MENGUE
RENAUD LEPLAIDEUR
Affiliation:
ISEA, Université de la Nouvelle-Caledonie, New Caledonia
JAIRO KRÁS MENGUE
Affiliation:
Departamento Interdisciplinar, Universidade Federal do Rio Grande do Sul, Tramandaí, Brazil
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Abstract

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 Walters potential, we show that perturbations of that potential that go faster to zero than the pressure do not change the selection, neither for the subaction nor for the limit measure, a zero temperature.

Keywords

ergodic optimizationselectionzero temperature

MSC classification

Primary: 37D35: Thermodynamic formalism, variational principles, equilibrium states
Secondary: 37A60: Dynamical systems in statistical mechanics

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , First View , pp. 1 - 35
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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