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Bibliographic Details
Main Authors: Juárez, Iker Martínez, Morgado, Héctor Sánchez
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2401.10335
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author Juárez, Iker Martínez
Morgado, Héctor Sánchez
author_facet Juárez, Iker Martínez
Morgado, Héctor Sánchez
contents For a sub-riemannian structure on the torus, satisfying the Hörmander condition, we consider the Mañé Lagrangian associated to a horizontal vector field. Assuming that the Aubry set consists in a finite number of static classes, we show that the invariant measure, for the horizontal stochastic perturbation of the flow of the vector field, determines a particular weak KAM solution of the Lagrangian, as the perturbation tends to zero.
format Preprint
id arxiv_https___arxiv_org_abs_2401_10335
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A selection of a weak KAM solution of the sub-riemannian Mañé Lagrangian
Juárez, Iker Martínez
Morgado, Héctor Sánchez
Dynamical Systems
37J51, 60F10, 49L25, 53C17
For a sub-riemannian structure on the torus, satisfying the Hörmander condition, we consider the Mañé Lagrangian associated to a horizontal vector field. Assuming that the Aubry set consists in a finite number of static classes, we show that the invariant measure, for the horizontal stochastic perturbation of the flow of the vector field, determines a particular weak KAM solution of the Lagrangian, as the perturbation tends to zero.
title A selection of a weak KAM solution of the sub-riemannian Mañé Lagrangian
topic Dynamical Systems
37J51, 60F10, 49L25, 53C17
url https://arxiv.org/abs/2401.10335