| 扭曲退化同宿分支 |
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| 引用本文： | 金银来.扭曲退化同宿分支[J].高校应用数学学报(英文版),2003,18(2):186-192. |
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| 作者姓名： | 金银来 |
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| 作者单位： | Jin YinlaiDept. of Math.，Linyi Teachers Univ.，Linyi 276005，China. Dept. of Math.，East China Normal Univ.，Shanghai 200062，China. |
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| 基金项目： | Supported by the National Natural Science Foundation of China(1 0 0 71 0 0 2 2 ) and the Shanghai PriorityAcademic Discipline |
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| 摘 要： | § 1 HypothesesConsider the following system:z.=f(z) , (1 .1 )and its perturbed systemz.=f(z) +g(z,μ) (1 .2 )where z∈ Rm+n,μ∈ Rk,k≥ 3,0≤ |μ| 1 ,f,g∈ Cr,r≥ 4 ,g(z,0 ) =0 .For simplicity,we sup-pose thatf(p) =0 ,g(p,μ) =0 .Moreover,for(1 .1 ) we assume(H1 ) The stable manifold Wspand the unstable manifold Wupof z=p are m-dimension-al and n-dimensional,respectively.The linearization Df(p) atthe equilibrium z=p has realmultiple-2 eigenvaluesλ1 and -ρ1 ,such thatany remaining eige…
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| 收稿时间： | 28 September 2002 |
Bifurcations of twisted homoclinic loops for degenerated cases |
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| Jin Yinlai.Bifurcations of twisted homoclinic loops for degenerated cases[J].Applied Mathematics A Journal of Chinese Universities,2003,18(2):186-192. |
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| Authors: | Jin Yinlai |
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| Institution: | (1) Dept. of Math., Linyi Teachers’ Univ., 276005 Linyi, China;(2) Dept. of Math., East China Normal Univ., 200062 Shanghai, China |
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| Abstract: | In this paper, the bifurcation problems of twisted and degenerated homoclinic loop for higher dimensional systems are studied.
Under the nonresonant condition, the existence, uniqueness, and incoexistence of the 1-homoclinic loop and 1-periodic orbit
near Γ are obtained, and the inexistence of the 2-homoclinic loop and the existence of 2-periodic orbit near Γ are also given.
Supported by the National Natural Science Foundation of China (100710022) and the Shanghai Priority Academic Disciplines. |
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| Keywords: | local coordinates bifurcation equation twist homoclinic loop bifurcation |
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