A cubic Hénon-like map in the unfolding of degenerate homoclinic orbit with resonance

In this Note, we study the unfolding of a vector field that possesses a degenerate homoclinic (of inclination-flip type) to a hyperbolic equilibrium point where its linear part possesses a resonance. For the unperturbed system, the resonant term associated with the resonance vanishes. After suitable rescaling, the Poincaré return map is a cubic Hénon-like map. We deduce the existence of a strange attractor which persists in the Lebesgue measure sense. We also show the presence of an attractor with topological entropy close to log 3.