| HOMOCLINIC BIFURCATION WITH CODIMENSION 3 |
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| 作者姓名： | Zhu Deming |
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| 作者单位： | Department of Matehematics，East China Normal University，Shanghai 200062，China |
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| 摘 要： | ＨＯＭＯＣＬＩＮＩＣＢＩＦＵＲＣＡＴＩＯＮＷＩＴＨＣＯＤＩＭＥＮＳＩＯＮ３￥ＺＨＵＤＥＭＩＮＧＡｂｓｔｒａｃｔ：ＦｉｒｓｔｉｔｉｓｐｒｏｖｅｄｔｈａｔｂｏｔｈｔｈｅｉｎｔｅｇｒａｌｏｆｔｈｅｄｉｖｅｒｇｅｎｃｅａｎｄｔｈｅＭｅｌｎｉｋｏｖｆｕｎｃｔｉ...
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| 关 键 词： | 同宿分布 余维数 半稳定 有限循环分支 |
| 收稿时间： | 1991/11/26 0:00:00 |
| 修稿时间： | 1992/4/24 0:00:00 |
HOMOCLINIC BIFURCATION WITH CODIMENSION 3 |
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| Zhu Deming.HOMOCLINIC BIFURCATION WITH CODIMENSION 3[J].Chinese Annals of Mathematics,Series B,1994,15(2):205-216. |
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| Authors: | Zhu Deming |
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| Institution: | DepartmentofMathematics,EastChinaNormalUniversity,Shanghai200062,China |
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| Abstract: | First it is proved that both the integral of the divergence and the
Melnikov function are invariants of the $C^2$ transformation. Then, the
problem of the planar homoclinic bifurcation with codimension $3$ is
considered. It is proved that, in a small neighborhood of the origin in
the parameter space of a $C^r$ ($r \ge 5$) system, there exist exactly
two $C^{r-1}$ semi-stable-limit-cycle branching surfaces, and their
common boundary is a unique $C^{r-1}$ three-multiple-limit-cycle
branching curve. The bifurcation pictures and the asymptotic expansions
of the bifurcation functions are given. The stability criterion for the
homoclinic loop is also obtained when the integral of the divergence is
zero. The proof of the auxiliary theorems will be presented in 16].
\endabstract |
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| Keywords: | Homoclinic bifurcation Codimension Semi-stable-limit-cycle branch Three- multiple-limit- cycle branch |
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