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arXiv · 2401.10335

A selection of a weak KAM solution of the sub-riemannian Ma\~n\'e Lagrangian

Iker Martínez Juárez·Héctor Sánchez Morgado
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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.

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Iker Martínez Juárez, Héctor Sánchez Morgado. 2024-01-18. A selection of a weak KAM solution of the sub-riemannian Ma\~n\'e Lagrangian. https://arxiv.org/abs/2401.10335

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