On two-dimensional Hamiltonian systems with sixth-order integrals of motion
Exactly Solvable and Integrable Systems
2022-11-17 v2 Mathematical Physics
Dynamical Systems
math.MP
Abstract
We obtain 21 two-dimensional natural Hamiltonian systems with sextic invariants, which are polynomial of the sixth order in momenta. Following to Bertrand, Darboux, and Drach these results of the standard brute force experiments can be applied to construct a new mathematical theory.
Keywords
Cite
@article{arxiv.2110.12860,
title = {On two-dimensional Hamiltonian systems with sixth-order integrals of motion},
author = {E. O. Porubov and A. V. Tsiganov},
journal= {arXiv preprint arXiv:2110.12860},
year = {2022}
}
Comments
LaTeX with amsfonts, 15 pages