In this paper we use the qualitative theory of planar differential equations to study a saddle-center bifurcation in one-parameter family of planar Hamiltonian vector fields. In particular, we show that the one-parameter family of Hamiltonian functions determines the phase portraits of these vector fields.
Aharonov-Bohm effect; Hamiltonian; vector fields; phase portrait; equilibrium points; singularities; bifurcations; homoclinic loops
