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Quasi-periodic solutions of the integrable dynamical systems related to Hill’s equation. (English) Zbl 0691.58022

The author considers the relationship between Hill’s equation and the Garnier-type systems. Finite-gap solutions to the Garnier system and to g-dimensional anisotropic harmonic oscillator in a radial quartic potential are presented. The interconnection between these solutions and solutions to Neumann-type systems is discussed.
Reviewer: Yu.E.Gliklikh

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.)
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