Elliptic functions and integrals. (Fonctions et intégrales elliptiques.)
Geodesic flow on , Kac-Moody Lie algebra and singularities in the complex t-plane.
The article studies geometrically the Euler-Arnold equations associatedto geodesic flow on for a left invariant diagonal metric. Such metric were first introduced by Manakov [17] and extensively studied by Mishchenko-Fomenko [18] and Dikii [6]. An essential contribution into the integrability of this problem was also made by Adler-van Moerbeke [4] and Haine [8]. In this problem there are four invariants of the motion defining in C = Lie( ⊗ C) an affine Abelian surface as complete intersection of...
The complex geometry of an integrable system
In this paper, a finite dimensional algebraic completely integrable system is considered. We show that the intersection of levels of integrals completes into an abelian surface (a two dimensional complex algebraic torus) of polarization and that the flow of the system can be linearized on it.
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