44 citations · 49 across the 9 of their papers we have counts for
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math.DG2004★ 2 cited
The geometry of nondegeneracy conditions in completely integrable systems
Nicolas Roy
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 coordin…
math.SG2004
Decomposition of symplectic vector fields with respect to a fibration in lagrangian tori
Nicolas Roy
Given a fibration of a symplectic manifold by lagrangian tori, we show that each symplectic vector field splits into two parts : the first is Hamiltonian and the second is symplect…
math-ph2004
A semi-classical K.A.M. theorem
Nicolas Roy
We consider a semi-classical completely integrable system defined by a -pseudodifferential operator on the torus . In order to study perturbed oper…