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Abstract view

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 $I_p(P,Q)$ of two complex projective curves $P(x,y,z) = 0$, $Q(x,y,z) = 0$ 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.