On maximally superintegrable systems

Details On maximally superintegrable systems On maximally superintegrable systems

2007-11-14

arxiv.org/abs/0711.2225v2

Regular and Chaotic Dynamics, v.13, n.3, 178-190, 2008

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages, LaTeX with AmsFonts

Scientific paper

10.1134/S1560354708030040

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 St\"ackel 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.

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