TL;DR
This paper discusses the construction of additional integrals of motion for maximally superintegrable systems, focusing on Stäckel systems and those related to quadratic r-matrix algebras, including Heisenberg magnet and Toda lattices.
Contribution
It presents methods for constructing single-valued integrals of motion for maximally superintegrable systems using action-angle variables.
Findings
Constructed additional integrals for Stäckel systems.
Extended methods to systems related to quadratic r-matrix algebras.
Applied constructions to Heisenberg magnet and Toda lattices.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.