QUADRATIC HAMILTONIAN VECTOR FIELDS

Joan C. Artés and Jaume Llibre

Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain.

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