On maximally superintegrable systems

Abstract

Locally any completely integrable system is maximally superintegrable system such as 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 Stäckel 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.

12 pages, LaTeX with AmsFonts

References in corpus (2)

• A family of the Poisson brackets compatible with the Sklyanin bracket
• The Poisson bracket compatible with the classical reflection equation algebra

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