St\"ackel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics
Exactly Solvable and Integrable Systems
2021-02-18 v3 Differential Geometry
Abstract
A non-degenerate second-order maximally conformally superintegrable system in dimension 2 naturally gives rise to a quadric with position dependent coefficients. It is shown how the system's St\"ackel class can be obtained from this associated quadric.The St\"ackel class of a second-order maximally conformally superintegrable system is its equivalence class under St\"ackel transformations, i.e., under coupling-constant metamorphosis.
Keywords
Cite
@article{arxiv.2010.03638,
title = {St\"ackel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics},
author = {Andreas Vollmer},
journal= {arXiv preprint arXiv:2010.03638},
year = {2021}
}