04-142 Andrzej J. Maciejewski, Maria Przybylska

Darboux Polynomials and First Integrals of Natural Polynomial Hamiltonian Systems (348K, postscript) May 3, 04

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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.

Files: 04-142.src( 04-142.keywords , pol_PhLA.ps )