The non-wandering set of some Henon maps

We consider the Henon maps h(a,b)(x,y) = (1 - ax(2) + y, bx). For \b\ is sm all and b < 0, there is a positive measure set of a values near 2, the corr esponding map exhibits a strange attractor Lambda(a,b). In this paper, we c onstruct a trapping region which contains Lambda(a,b) we give an exact desc ription of the basin of these Henon strange attractors Lambda(a,b) and we a lso describe the non-wandering set of h(a,b) as the union of Lambda(a,b) wi th a fixed point. (C) 2000 Elsevier Science Ltd. All rights reserved.