本文考虑Lauwerier映射Fa，b（X，y）=（bx（1-2y）+y，ay（l-y））。我们证明对于参数a在一个正测度集合中，对应的映射有非平凡的拓扑可迁的吸引子A，其中A是某个双曲不动点的不稳定集的闭包。周期点是双曲的且在A中稠密，而且A中任两个周期点异宿相关（稳定与不稳定集的横截相交）。同时也构造支撑在吸引子上的Sinai-Bowen-Ruelle测度，并研究其性质。

We consider the Henon 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 Henon strange attractors Λa, b.

We consider the Henon maps ha,b…(x,y)=(1-ax2) 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 Ka;b. In this paper, we construct a trapping region which contains Λa;b, we give an exact description of the basin of these Henon 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.