Darboux Polynomials and First Integrals of Natural Polynomial Hamiltonian Systems
Dynamical Systems
2015-06-26 v2 Mathematical Physics
Classical Analysis and ODEs
math.MP
Exactly Solvable and Integrable Systems
Abstract
We show that for a natural polynomial Hamiltonian system the existence of a single Darboux polynomial (a partial polynomial first integral) is equivalent to the existence of an additional first integral functionally independent with the Hamiltonian function. Moreover, we show that, in a case when the degree of potential is odd, the system does not admit any proper Darboux polynomial, i.e., the only Darboux polynomials are first integrals.
Cite
@article{arxiv.math/0404366,
title = {Darboux Polynomials and First Integrals of Natural Polynomial Hamiltonian Systems},
author = {Andrzej J. Maciejewski and Maria Przybylska},
journal= {arXiv preprint arXiv:math/0404366},
year = {2015}
}
Comments
14 pages, typos corrected