7 papers
Weak K.A.M. solutions and minimizing orbits of twist maps
Marie-Claude Arnaud, Maxime Zavidovique
For exact symplectic twist maps of the annulus, we etablish a choice of weak K.A.M. solutions that depend in a Lipschitz-continuous way on the cohomology class $c…
Actions of symplectic homeomorphisms/diffeomorphisms on foliations by curves in dimension 2
Marie-Claude Arnaud, Maxime Zavidovique
The two main results of this paper concern the regularity of the invariant foliation of a C0-integrable symplectic twist diffeomorphisms of the 2-dimensional annulus, namely that $…
Twisted Lax--Oleinik formulas and weakly coupled systems of Hamilton--Jacobi equations
Maxime Zavidovique
We show that viscosity solutions of evolutionary weakly coupled systems of Hamilton--Jacobi equations can be approximated by iterated twisted Lax--Oleinik like operators. We establ…
Fixed points of contractions approximating 1-Lipschitz maps
Maxime Zavidovique
A -Lipschitz map from a convex compact set to itself has fixed points. This consequence of Brouwer's or Schauder's fixed point theorem has more elementary proofs by approxim…
On the transversal dependence of weak K.A.M. solutions for symplectic twist maps
Marie-Claude Arnaud, Maxime Zavidovique
For a symplectic twist map, we prove that there is a choice of weak K.A.M. solutions that depend in a continuous way on the cohomology class. We thus obtain a continuous function $…
Convergence of the solutions of discounted Hamilton--Jacobi systems
Andrea Davini, Maxime Zavidovique
We consider a weakly coupled system of discounted Hamilton--Jacobi equations set on a closed Riemannian manifold. We prove that the corresponding solutions converge to a specific s…