Reciprocal transformations for Stackel-related Liouville integrable systems
Exactly Solvable and Integrable Systems
2007-05-23 v1 Mathematical Physics
math.MP
Symplectic Geometry
Abstract
We consider the St\"ackel transform, also known as the coupling-constant metamorphosis, which under certain conditions turns a Hamiltonian dynamical system into another such system and preserves the Liouville integrability. We show that the corresponding transformation for the equations of motion is nothing but the reciprocal transformation of a special form and we investigate the properties of this transformation. This result is further applied for the study of the -hole deformations of the Benenti systems or more general seed systems.
Keywords
Cite
@article{arxiv.nlin/0607057,
title = {Reciprocal transformations for Stackel-related Liouville integrable systems},
author = {Maciej Blaszak and Artur Sergyeyev},
journal= {arXiv preprint arXiv:nlin/0607057},
year = {2007}
}
Comments
12 pages, no figures