In this paper, we give some examples to show that the relation among Milnor attractor and the support of nature measure and riddling attractor

We consider the Henon-like strange attractors Λ in a family which is a nonsingular perturbation of a d-modal family. The existence of the Henon-like strange attractors in this family was proved by Diaz et al. [Inventions Math. 125 (1996) 37]. We prove that the transversal homoclinic points are dense in Λ, and that hyperbolic periodic points are dense in Λ. Moreover, the hyperbolic periodic points that are heteroclinically related to the primary periodic point (transversal intersection of stable and unstable manifolds) are dense in Λ.

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.

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.

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 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.

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。

In this paper, the structure of the strange attractors in the Lozi map is investigated on basis of the results gotten by the authors in 1991-1993. The new results of the strange attractors of the Lozi map show that our viewpoint is correct.