A selection of a weak KAM solution of the sub-riemannian Ma\~n\'e Lagrangian
Dynamical Systems
2026-05-13 v3
Abstract
For a sub-riemannian structure on the torus, satisfying the H\"ormander condition, we consider the Ma\~n\'e 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.
Cite
@article{arxiv.2401.10335,
title = {A selection of a weak KAM solution of the sub-riemannian Ma\~n\'e Lagrangian},
author = {Iker Martínez Juárez and Héctor Sánchez Morgado},
journal= {arXiv preprint arXiv:2401.10335},
year = {2026}
}
Comments
9 pages