English

Finiteness of integrable $n$-dimensional homogeneous polynomial potentials

Exactly Solvable and Integrable Systems 2010-04-19 v1

Abstract

We consider natural Hamiltonian systems of n>1n>1 degrees of freedom with polynomial homogeneous potentials of degree kk. We show that under a genericity assumption, for a fixed kk, 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 kk.

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}
}
R2 v1 2026-07-22T18:16:38.327Z