Normal Form for the Schrödinger equation with analytic non--linearities

Abstract

In this paper we discuss a class of normal forms of the completely resonant non--linear Schrödinger equation on a torus. We stress the geometric and combinatorial constructions arising from this study. Further analytic considerations and applications to quasi--periodic solutions will appear in a forthcoming article. This paper replaces a previous version correcting some mistakes.

52 pages, 2 figures

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