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Isospectral Hamiltonian flows in finite and infinite dimensions. I: Generalized Moser systems and moment maps into loop algebras. (English) Zbl 0659.58022
The authors provide a systematic link between finite dimensional integrable systems, flows in loop algebras and “integrable” partial differential equations through the use of moment maps. In particular they use the theory of Adler-Kostant-Symes on Hamiltonian systems on coadjoint orbits to produce a large class of commuting flows of isospectral type that are generalizations of the rank two perturbations considered by J. Moser [Differential geometry, Proc. int. Chern Symp., Berkeley 1979, 147-188 (1980; Zbl 0455.58018)].
Reviewer: H.Knörrer

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.)
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
37C10 Dynamics induced by flows and semiflows
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