A selection of a weak KAM solution of the sub-riemannian Mañé Lagrangian

2024/01/18 by Iker Martínez Juárez, Juárez, Iker Martínez, Héctor Sánchez-Morgado +1
Mathematics · Economics, Econometrics and Finance · #Stochastic processes and statistical mechanics #Stochastic processes and financial applications #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2401.10335

Abstract

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.

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