Finiteness of integrable $n$-dimensional homogeneous polynomial potentials
Exactly Solvable and Integrable Systems
2010-04-19 v1
Abstract
We consider natural Hamiltonian systems of degrees of freedom with polynomial homogeneous potentials of degree . We show that under a genericity assumption, for a fixed , at most only a finite number of such systems is integrable. We also explain how to find explicit forms of these integrable potentials for small .
Keywords
Cite
@article{arxiv.nlin/0701059,
title = {Finiteness of integrable $n$-dimensional homogeneous polynomial potentials},
author = {Maria Przybylska},
journal= {arXiv preprint arXiv:nlin/0701059},
year = {2010}
}