- 04-142 Andrzej J. Maciejewski, Maria Przybylska
- Darboux Polynomials and First Integrals of Natural Polynomial Hamiltonian Systems
May 3, 04
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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.