# The geometry of nondegeneracy conditions in completely integrable systems (corrected version of fascicule 4, volume XIV, 2005, p. 705-719)

Nicolas Roy^{[1]}

- [1] Geometric Analysis Group, Institut für Mathematik, Humboldt Universität, Rudower Chaussee 25, Berlin D-12489, Germany.

Annales de la faculté des sciences de Toulouse Mathématiques (2006)

- Volume: 15, Issue: 2, page 383-397
- ISSN: 0240-2963

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topRoy, Nicolas. "The geometry of nondegeneracy conditions in completely integrable systems (corrected version of fascicule 4, volume XIV, 2005, p. 705-719)." Annales de la faculté des sciences de Toulouse Mathématiques 15.2 (2006): 383-397. <http://eudml.org/doc/10051>.

@article{Roy2006,

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.},

affiliation = {Geometric Analysis Group, Institut für Mathematik, Humboldt Universität, Rudower Chaussee 25, Berlin D-12489, Germany.},

author = {Roy, Nicolas},

journal = {Annales de la faculté des sciences de Toulouse Mathématiques},

keywords = {KAM theorems; geometrical formulation; fibration of a symplectic manifold; Lagrangian tori; nondegenerate Hamiltonians},

language = {eng},

number = {2},

pages = {383-397},

publisher = {Université Paul Sabatier, Toulouse},

title = {The geometry of nondegeneracy conditions in completely integrable systems (corrected version of fascicule 4, volume XIV, 2005, p. 705-719)},

url = {http://eudml.org/doc/10051},

volume = {15},

year = {2006},

}

TY - JOUR

AU - Roy, Nicolas

TI - The geometry of nondegeneracy conditions in completely integrable systems (corrected version of fascicule 4, volume XIV, 2005, p. 705-719)

JO - Annales de la faculté des sciences de Toulouse Mathématiques

PY - 2006

PB - Université Paul Sabatier, Toulouse

VL - 15

IS - 2

SP - 383

EP - 397

AB - 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.

LA - eng

KW - KAM theorems; geometrical formulation; fibration of a symplectic manifold; Lagrangian tori; nondegenerate Hamiltonians

UR - http://eudml.org/doc/10051

ER -

## References

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