QUADRATIC HAMILTONIAN VECTOR FIELDS

JOAN C. ARTÉS AND JAUME LLIBRE


Abstract


Let $H$ be a cubic polynomial in two variables over $\Bbb R$. Then $H$ defines a quadratic Hamiltonian vector field $(\partial H/\partial y,-\partial H/\partial x)$. The purpose of this paper is to prove that there are exactly 28 non--equivalent topologic phase portraits of quadratic Hamiltonian vector fields.