Suppose F and G are [tex]c^2[/tex] and [tex] F_x = F_y = G_x = G_y = 0 [/tex] at the origin. Must the origin be an asymptotically stable equilibrium point? One more Give an explicit example of a DE with exactly two saddle points and no other equilibria. Anybody? Could I work backwards starting with the eigenvalues to form a system that has the two saddle points? This might be a dumb question.