A new estimate on Evans' Weak KAM approach

TL;DR

This paper explores Evans' recent formulation of weak KAM theory, providing explicit computations in one-dimensional cases to illustrate geometric insights and establishing new lower bounds that extend to systems with multiple degrees of freedom.

Contribution

It offers explicit calculations for Evans' weak KAM theory in one dimension and introduces new lower bounds applicable to higher-dimensional systems.

Findings

Explicit computations in 1D illustrate geometric content.

New lower bounds extend to systems with multiple degrees of freedom.

The approach enhances understanding of weak KAM theory's geometric aspects.

Abstract

We consider a recent formulation of weak KAM theory proposed by Evans. As well as for classical integrability, for one dimensional mechanical Hamiltonian systems all the computations can be explicitly done. This allows us on the one hand to illustrate the geometric content of the theory, on the other hand to prove new lower bounds which extend also to the generic n degrees of freedom case.