# American Institute of Mathematical Sciences

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September  2017, 37(9): 4625-4636. doi: 10.3934/dcds.2017199

## Analytic dependence on parameters for Evans' approximated Weak KAM solutions

 1 Dipartimento di Matematica "Tullio Levi-Civita", Università degli Studi di Padova, Via Trieste, 63 -35121 Padova, Italy 2 Department of Mathematics, The University of Tulsa, 800 South Tucker Drive, Tulsa -Oklahoma 74104, USA

Received  June 2016 Revised  April 2017 Published  June 2017

We consider a variational principle for approximated Weak KAM solutions proposed by Evans. For Hamiltonians in quasi-integrable form $h(p)+\varepsilon f(\varphi,p)$, we prove that the map which takes the parameters $(\varepsilon,P,\varrho)$ to Evans' approximated solution $u_{\varepsilon,P,\varrho}$ 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 $\varepsilon$.

Citation: Olga Bernardi, Matteo Dalla Riva. Analytic dependence on parameters for Evans' approximated Weak KAM solutions. Discrete & Continuous Dynamical Systems - A, 2017, 37 (9) : 4625-4636. doi: 10.3934/dcds.2017199
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