English

On maximally superintegrable systems

Exactly Solvable and Integrable Systems 2010-06-22 v2

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 rr-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

Cite

@article{arxiv.0711.2225,
  title  = {On maximally superintegrable systems},
  author = {A. V. Tsiganov},
  journal= {arXiv preprint arXiv:0711.2225},
  year   = {2010}
}

Comments

12 pages, LaTeX with AmsFonts

R2 v1 2026-06-21T09:43:23.764Z