A Note on Darboux Polynomials of Monomial Derivations

Abstract

We study a monomial derivation $d$ proposed by J. Moulin Ollagnier and A. Nowicki in the polynomial ring of four variables, and prove that $d$ has no Darboux polynomials if and only if $d$ has a trivial field of constants.

References in corpus (1)

• Darboux Polynomials and First Integrals of Natural Polynomial Hamiltonian Systems