Summing up the Dynamics of Quadratic Hamiltonian Systems With a Center

In this work we study the global geometry of planar quadratic Hamiltonian systems with a center and we sum up the dynamics of these systems in geometrical terms. For this we use the algebro-geometric concept of multiplicity of intersection Ip(POQ) of two complex projective curves P(xO yO z) = 0, Q(xO yO z) = 0 at a point p of the plane. This is a convenient concept when studying polynomial systems and it could be applied for the analysis of other classes of nonlinear systems. The work of the second author was partially supported by NSERC and both authors were partially supported by Quebec Education Ministry. Received by the editors March 16, 1995. AMS subject classification: 34C, 58F. c Canadian Mathematical Society 1997. 582