The basin of the strange attractors of some Hénon maps

We consider the Hénon maps. 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 and prove this trapping is contained in the basin of Λa,b. Furthermore we give an exact description of the basin of these Hénon strange attractors Λa,b.