A selection principle for a viscosity solution of the Mañé Lagrangian

Iker Martínez Juárez, Héctor Sánchez Morgado

Published 2024-01-18Version 1

For a vector field on a compact manifold we consider the invariant measure for the stochastic perturbation as well as the corresponding Ma\~n\'e lagrangian. We show that the limit of the invariant measure of the perturbated system, when the perturbation tends to zero, determines a particular weak KAM solution of the lagrangian.