## On a version of the Arnold-Liouville theorem in infinite dimension : a case study

### Jeudi 4 mai 2017 10:30-11:30 - Thomas Kappeler - Université de Zurich

Résumé : It is well known that the focusing nonlinear Schroedinger (fNLS) equation is an integrable PDE. When considered on the circle, the periodic eigenvalues of the Zakharov-Shabat (ZS) operator, appearing in the Lax pair formulation of the fNLS equation, form an infinite set of integrals of motion. In contrast to other integrable PDEs such as the defocusing nonlinear Schr\”odinger equation, the fNLS equation exhibits features of hyperbolic dynamics, in particular homoclinic orbits. In this talk I present a version of the Arnold-Liouville theorem for the fNLS equation : any connected level set of the above mentioned integrals of maximal — hence necessarily infinite — dimension is a torus. On an invariant open neighborhood of such a torus we construct normal coordinates by developing the method of analytic continuation in the framework of normal form theory.

Lieu : Salle 117-119, Bâtiment 425

On a version of the Arnold-Liouville theorem in infinite dimension : a case study  Version PDF
septembre 2020 :
 Département de Mathématiques Bâtiment 307 Faculté des Sciences d'Orsay Université Paris-Saclay F-91405 Orsay Cedex Tél. : +33 (0) 1-69-15-79-56 Département Fermeture du département Laboratoire Formation