Generalized St\"ackel Transform and Reciprocal Transformations for Finite-Dimensional Integrable Systems
Exactly Solvable and Integrable Systems
2008-11-26 v4 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
We present a multiparameter generalization of the St\"ackel transform (the latter is also known as the coupling-constant metamorphosis) and show that under certain conditions this generalized St\"ackel transform preserves the Liouville integrability, noncommutative integrability and superintegrability. The corresponding transformation for the equations of motion proves to be nothing but a reciprocal transformation of a special form, and we investigate the properties of this reciprocal transformation. Finally, we show that the Hamiltonians of the systems possessing separation curves of apparently very different form can be related through a suitably chosen generalized St\"ackel transform.
Cite
@article{arxiv.0706.1473,
title = {Generalized St\"ackel Transform and Reciprocal Transformations for Finite-Dimensional Integrable Systems},
author = {Artur Sergyeyev and Maciej Blaszak},
journal= {arXiv preprint arXiv:0706.1473},
year = {2008}
}