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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 ‡
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-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 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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【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】A note about Milnor attractor and riddled basin
曹永罗, Yongluo Cao *
Chaos, Solitons and Fractals 19(2004)759-764,-0001,():
-1年11月30日
In this paper, we give some examples to show that the relation among Milnor attractor and the support of nature measure and riddling attractor
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【期刊论文】Lauwerier映射的奇怪吸引子的遍历性及其结构
曹永罗
中国科技论文在线,1999,42(6):965~968,-0001,():
-1年11月30日
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。
Lauwerier映射, 奇怪吸引子, Sinai-Bowen-Ruelle(, SBR), 测度
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