The density of the transversal homoclinic points in the Henon-like strangeattractors

We consider the Henon-like strange attractors Lambda in a family which is a nonsingular perturbation of a d-modal family. The existence of the Henon-l ike strange attractors in this family was proved by Diaz et al. [Inventions Math. 125 (1996) 37]. We prove that the transversal homoclinic points are dense in Lambda, and that hyperbolic periodic points are dense in Lambda. M oreover, the hyperbolic periodic points that are heteroclinically related t o the primary periodic point (transversal intersection of stable and unstab le manifolds) are dense in Lambda. (C) 2001 Published by Elsevier Science L td.