This paper is based on the presentation done at seminar Laurent Schwartz in January 2020. It describes and summarizes results given Rational normal forms stability of small solutions to nonlinear Schrödinger equations, see [BFG20a], written with Joackim Bernier Benoît Grébert, published Annals PDE 6, article number: 14 (2020) 65p. We describe here main arguments proof as well general strategy u...

Integrable or near-integrable magnetic fields are prominent in the design of plasma confinement devices. Such a field is characterized by existence singular foliation entirely consisting invariant submanifolds. A compact regular leaf (a flux surface) this must be diffeomorphic to two-torus. In neighborhood surface, it known that admits several exact smooth normal forms which lines straight. How...