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 -matrix algebras are discussed. Among these system there are the open Heisenberg magnet and the open Toda lattices associated with the different root systems.
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