Periodically forced double homoclinic loops to a dissipative saddle (Q2634269)

The author considers small \(t\)-periodic perturbations of the planar autonomous system \[ \dot{x}=-\alpha x+f(x,y),\quad \dot{y}=\beta y+g(x,y) \] assuming that the nonperturbed system has two homoclinic loops to the rest point \((0,0)\). It is shown that the perturbed system may have attractive quasi-periodic tori, Newhouse sinks, Hénon-like attractors, etc. The theory is applied to the perturbed Duffing equation.