6 papers · 1 filter
Integrability for conformally symplectic systems
Marie-Claude Arnaud, Xifeng Su, Maxime Zavidovique
The goal of this paper is to study the dynamics of conformally symplectic Hamiltonian flows under the light of integrability. As the dynamics of conformally symplectic Hamiltonian…
Discrete and Continuous Weak KAM Theory: an introduction through examples and its applications to twist maps
Maxime Zavidovique
The aim of these notes is to present a self contained account of discrete weak KAM theory. Put aside the intrinsic elegance of this theory, it is also a toy model for classical wea…
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 $…
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 $…
Strict sub-solutions and Mañe potential in discrete weak KAM theory
Maxime Zavidovique
In this paper, we explain some facts on the discrete case of weak KAM theory. In that setting, the Lagrangian is replaced by a cost , on a "reasonable"…