14 citations · 58 across the 28 of their papers we have counts for
30 papers
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…
Conformally symplectic Dynamics
Marie-Claude Arnaud
Dynamists have been studying Hamiltonian systems for a long time. However, many physical systems are dissipative and do not preserve a symplectic form. This is the case, for exampl…
The dynamics of conformal Hamiltonian flows: dissipativity and conservativity
Simon Allais, Marie-Claude Arnaud
We study in detail the dynamics of conformal Hamiltonian flows that are defined on a conformal symplectic manifold (this notion was popularized by Vaisman in 1976). We show that th…
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…
Vanishing asymptotic Maslov index for conformally symplectic flows
Marie-Claude Arnaud, Anna Florio, Valentine Roos
Motivated by Mather theory of minimizing measures for symplectic twist dynamics, we study conformally symplectic flows on a cotangent bundle. These dynamics are the most general dy…
On the fragility of periodic tori for families of symplectic twist maps
Marie-Claude Arnaud, Jessica Elisa Massetti, Alfonso Sorrentino
In this article we study the fragility of Lagrangian periodic tori for symplectic twist maps of the -dimensional annulus and prove a rigidity result for completely integrable o…