The geometry of nondegeneracy conditions in completely integrable systems (corrected version of fascicule 4, volume XIV, 2005, p. 705-719)
Nicolas Roy (2006)
Annales de la faculté des sciences de Toulouse Mathématiques
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Nondegeneracy conditions need to be imposed in K.A.M. theorems to insure that the set of diophantine tori has a large measure. Although they are usually expressed in action coordinates, it is possible to give a geometrical formulation using the notion of regular completely integrable systems defined by a fibration of a symplectic manifold by lagrangian tori together with a Hamiltonian function constant on the fibers. In this paper, we give a geometrical definition of different nondegeneracy...