Extensions of non-natural Hamiltonians
Mathematical Physics
2020-10-28 v1 math.MP
Exactly Solvable and Integrable Systems
Abstract
The concept of extended Hamiltonian systems allows the geometrical interpretation of several integrable and superintegrable systems with polynomial first integrals of degree depending on a rational parameter. Until now, the procedure of extension has been applied only in the case of natural Hamiltonians. In this article, we give several examples of application to non-natural Hamiltonians, such as the two point-vortices, the Lotka-Volterra and some quartic in the momenta Hamiltonians, obtaining effectively extended Hamiltonians in some cases and failing in others. We briefly discuss the reasons of these results.
Keywords
Cite
@article{arxiv.2001.04152,
title = {Extensions of non-natural Hamiltonians},
author = {Claudia Maria Chanu and Giovanni Rastelli},
journal= {arXiv preprint arXiv:2001.04152},
year = {2020}
}
Comments
11 pages