| 一类余维3的鞍-焦点异宿环分支 |
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| 作者单位： | 华东师范大学数学系，华东师范大学数学系 上海 200062，上海 200062 |
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| 摘 要： | 对余维3系统X_μ(x)具有包含一个双曲鞍-焦点O_1和一个非双曲鞍-焦点O_2的异宿环f进行了研究.证明了在f的邻域内有可数无穷条周期轨线和异宿轨线,当非粗糙异宿轨线Γ~0破裂时X_μ(x)会产生同宿轨分支,并给出了相应的分支曲线和两种同宿环共存的参数值.在3参数扰动下Γ~0破裂和O_2点产生Hopf分支的情况下,在f的邻域内有一条含O_1点同宿环,可数无效多条的轨线同宿于O_2点分支出的闭轨H_0,一条或无穷多条(可数或连续统的)异宿轨线等.
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| 关 键 词： | 异宿环 同宿环 极限环 分支曲面 Hopf分支 |
A Codimension 3 Bifurcation of Heteroclinic Contour Involving a Hyperbolic and a Non-hyperbolic Saddle-foci |
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| Authors: | DENG Guifeng ZHU Deming |
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| Institution: | DENG Guifeng~* ZHU Deming~* *Department of Mathematics,East China Normal University,Shanghai 200062,China. |
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| Abstract: | The codimension 3 bifurcations associated with a heteroclinic contour formed with two saddle-loci(among which,one is a weak saddle-focus)and two of their heteroclinic orbits are studied.In certain neighborhood of the contour,the existence of countably infinite 1-periodic orbits and 1(1/2)-heteroclinic orbits is given for the unperturbed system.Meanwhile, the complicated bifurcation patterns under the generic 3-parameter perturbation are also established,such as the Hopf bifurcation,1-homoclinic bifurcation,1-heteroclinic bifurca- tion,1(1/2)-heteroclinic bifurcation and the coexistence of different kinds of bifurcated orbits, etc..Furthermore,the number of the produced homoclinic or herteroclinic orbits can be finite,denumerable infinite or uncountable infinite,etc.. |
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| Keywords: | Heteroclinic contour Homoclinic orbit Limit cycle Bifurcation surface Hopf bifurcation |
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