The non-wandering set of some Hénon maps

We consider the Hénon maps ha,b(x,y)=(1−ax2+y,bx). For b is small and b<0, there is a positive measure set of a values near 2, the corresponding map exhibits a strange attractor Λa,b. In this paper, we construct a trapping region which contains Λa,b, we give an exact description of the basin of these Hénon strange attractors Λa,b and we also describe the non-wandering set of ha,b as the union of Λa,b with a fixed point.