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 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.

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.

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.

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.