Analytic dependence on parameters for Evans' approximated Weak KAM solutions

Abstract

We consider a variational principle for approximated Weak KAM solutions proposed by Evans. For Hamiltonians in quasi-integrable form, we prove that the map which takes the parameters to Evans\u2019 approximated solution is real analytic. In the mechanical case, we compute a recursive system of periodic partial differential equations identifying univocally the coefficients for the power series of the perturbative parameter