On Maximally Superintegrable Systems

    2008, Volume 13, Number 3, pp.  178-190

    Author(s): Tsiganov A. V.

    Locally any completely integrable system is maximally superintegrable system since we have the necessary number of the action-angle variables. The main problem is the construction of the single-valued additional integrals of motion on the whole phase space by using these multi-valued action-angle variables. Some constructions of the additional integrals of motion for the St├Ąckel systems and for the integrable systems related with two different quadratic $r$-matrix algebras are discussed. Among these system there are the open Heisenberg magnet and the open Toda lattices associated with the different root systems.
    Keywords: superintegrable systems, Toda lattices, Stackel systems
    Citation: Tsiganov A. V., On Maximally Superintegrable Systems, Regular and Chaotic Dynamics, 2008, Volume 13, Number 3, pp. 178-190

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