The geometry of nondegeneracy conditions in completely integrable systems
Differential Geometry
2016-09-07 v1 Symplectic Geometry
Abstract
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 conditions, we show the implication relations that exist between them, and we show the uniqueness of the fibration for non-degenerate Hamiltonians.
Keywords
Cite
@article{arxiv.math/0403412,
title = {The geometry of nondegeneracy conditions in completely integrable systems},
author = {Nicolas Roy},
journal= {arXiv preprint arXiv:math/0403412},
year = {2016}
}