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Classification des actions hamiltoniennes complètement intégrables de rang deux. (Classification of completely integrable Hamiltonian actions of rang 2.). (French) Zbl 0711.58017

According to the definition of A. S. Mishchenko and A. T. Fomenko [Funkts. Anal. Prilozh. 12, No.2, 46-56 (1978; Zbl 0396.58003)] the action of a Lie group G is completely integrable if it is locally free in a point, at least, and if the dimension of the manifold is the sum of the dimension and the rank of G. This highly abstract paper presents the proof of the following theorem. Let G be a compact connected Lie group of rank two, and \(M_ 1\) and \(M_ 2\) two manifolds on which the action of G is completely integrable; assume that these manifolds have the same image by the moment map, and that their principal isotropy groups are the same, then there exists a symplectic G-equivariant isomorphism of one onto the other.
Reviewer: M.Farkas

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.)
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
57S15 Compact Lie groups of differentiable transformations
22E20 General properties and structure of other Lie groups

Citations:

Zbl 0396.58003
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References:

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