A cubic Henon-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 resealing, the Poincare return map is a cubic Henon-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 (c) 2005 Academic des sciences. Published by Elsevier SAS. All rights reserved.