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【期刊论文】THE TRANSVERSAL HOMOCLINIC POINTS ARE DENSE IN THE CODIMENSION-1 HENON-LIKE STRANGE ATTRACTORS
曹永罗, YONGLUO CAO
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 127 (6): 1877~1883,-0001,():
-1年11月30日
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.
Henon-like strange attractor, transversal homoclinic point.,
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【期刊论文】The non-wandering set of some Henon maps
曹永罗, Yongluo Cao a, b, *, Jian Min Mao b
Chaos, Solitons and Fractals 11(2000)2045-2053,-0001,():
-1年11月30日
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.
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【期刊论文】The isolated saddle-node bifurcation occurring inside a horseshoe
曹永罗, Yongluo CaoYongluo Cao †, Shin Kiriki ‡
,-0001,():
-1年11月30日
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.
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【期刊论文】The Geometric Structure of Strange Attractors in the Lozi Mapl6
曹永罗, Yongluo CA, Zengrong LIU *
Communications in Nonlinear Science & Numerical Simulation, 1998, 3 (2): 119~123,-0001,():
-1年11月30日
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.
strange attractor, transversal homoclinic point, weak transversal homoclinic point
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【期刊论文】The density of the transversal homoclinic points in the Henon-like strange attractors
曹永罗, Yongluo Cao a, l, Shin Kiriki b, *
Chaos, Solitons and Fractals 13(2002)665-671,-0001,():
-1年11月30日
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.
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