Singular Lagrangian foliation associated to an integrable Hamiltonian vector field. (English) Zbl 0731.58038

Desolneux-Moulis, Nicole

Symplectic geometry, groupoids, and integrable systems, Sémin. Sud- Rhodan. Geom. VI, Berkeley/CA (USA) 1989, Math. Sci. Res. Inst. Publ. 20, 129-136 (1991).

[For the entire collection see Zbl 0722.00026.]
It is demonstrated that the geometry of an integrable Hamiltonian system follows rather “generic assumptions”. These hypotheses allow to study higher codimension singularities.

Reviewer: B.G.Konopelchenko (Novosibirsk)

MSC:

37J35	Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10	Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37C85	Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)

Keywords:

foliation; singular lagrangian; integrable vector fields; integrable Hamiltonian system