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arXiv · 0711.2225

On maximally superintegrable systems

A. V. Tsiganov
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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 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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A. V. Tsiganov. 2007-11-14. On maximally superintegrable systems. https://doi.org/10.1134/s1560354708030040

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