Time-periodic perturbation of a Liénard equation with an unbounded homoclinic loop

► Periodic perturbations of planar homoclinic loops can lead to chaotic dynamics. ► Planar polynomial vector fields may present unbounded homoclinic loops. ► Unbounded homoclinic loops can be studied with the Poincaré compactification. ► Periodic perturbations of unbounded homoclinic loops can also lead to chaos. ► The proof is made using the Melnikov method.