In this paper, we consider a smooth arc of diffeomorphisms which has a saddle-node bifurcation inside a nontrivial invariant set which is a deformation of a horseshoe. We show that this saddle-node bifurcation is isolated, that is, its hyperbolicity is maintained before and after the saddle-node bifurcation. Moreover we construct a C2-open set of arcs having the same property.

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 codimension-1 Henon-like strange attractors. We prove that the transversal homoclinic points are dense in, and that hyperbolic periodic points are dense in. Moreover the hyperbolic periodic points that are heteroclinically related to the primary fixed point (transversal intersection of stable and unstable manifolds) are dense in.