Existence of generic cubic homoclinic tangencies for Henon maps

In this paper, we show that the Henon map phi(a, b) has a generically unfolding cubic tangency for some (a, b) arbitrarily close to (-2, 0) by applying results of Gonchenko, Shilnikov and Turaev [On models with non-rough Poincare homoclinic curves. Physica D 62(1-4) (1993), 1-14; Dynamical phenomena in systems with structurally unstable Poincare homoclinic orbits. Chaos 6(1) (1996), 15-31; On Newhouse domains of two-dimensional diffeomorphisms which are close to a diffeomorphism with a structurally unstable heteroclinic cycle. Proc. Steklov Inst. Math. 216 (1997), 70-118; Homoclinic tangencies of an arbitrary order in Newhouse domains. Itogi Nauki Tekh. Ser. Sovrem. Mat. Prilozh. 67 (1999), 69-128, translation in J. Math. Sci. 105 (2001), 1738-1778; Homoclinic tangencies of arbitrarily high orders in conservative and dissipative two-dimensional maps. Nonlinearity 20 (2007), 241-275]. Combining this fact with theorems in Kiriki and Soma [Persistent antimonotonic bifurcations and strange attractors for cubic homoclinic tangencies. Nonlinearity 21(5) (2008), 1105-1140], one can observe the new phenomena in the Henon family, appearance of persistent antimonotonic tangencies and cubic polynomial-like strange attractors.