| Bifurcations of Fine 3-point-loop in Higher Dimensional Space |
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| 摘 要： |
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| 关 键 词： | 局部坐标系 线性变量方程 3点环 1-周期轨道 表面分支 |
| 收稿时间： | 2001-10-08 |
Bifurcations of Fine 3–point–loop in Higher Dimensional Space |
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| Yin Lai Jin,De Ming Zhu. Bifurcations of Fine 3–point–loop in Higher Dimensional Space[J]. Acta Mathematica Sinica(English Series), 2005, 21(1): 39-52. DOI: 10.1007/s10114-004-0400-9 |
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| Authors: | Yin Lai Jin De Ming Zhu |
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| Affiliation: | (1) Department of Mathematics, Linyi Teachers’ University, Linyi 276005, P. R. China;(2) Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China;(3) Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China |
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| Abstract: | By using the linear independent fundamental solutions of the linear variational equation along the heteroclinic loop to establish a suitable local coordinate system in some small tubular neighborhood of the heteroclinic loop, the Poincaré map is constructed to study the bifurcation problems of a fine 3–point loop in higher dimensional space. Under some transversal conditions and the non–twisted condition, the existence, coexistence and incoexistence of 2–point–loop, 1–homoclinic orbit, simple 1–periodic orbit and 2–fold 1–periodic orbit, and the number of 1–periodic orbits are studied. Moreover, the bifurcation surfaces and existence regions are given. Lastly, the above bifurcation results are applied to a planar system and an inside stability criterion is obtained. This work is supported by the National Natural Science Foundation of China (10371040), the Shanghai Priority Academic Disciplines and the Scientific Research Foundation of Linyi Teacher’s University |
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| Keywords: | Local coordinates Poincaré map 1– homoclinic orbit 1– periodic orbit Bifurcation surface |
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