| Existence and bifurcation of integral manifolds with applications |
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| 作者姓名： | HAN Mao'an & CHEN Xianfeng |
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| 作者单位： | HAN Mao'an & CHEN Xianfeng Department of Mathematics，Shanghai Normal University，Shanghai 200234，China，Department of Mathematics，Shanghai Jiao Tong University，Shanghai 200030，China |
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| 基金项目： | 国家自然科学基金，the Fund of the Ministry of Education of China |
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| 摘 要： | In this paper a bifurcation theorem on the existence of integral manifolds is obtained by using contracting principle. As an application, sufficient conditions for a higher dimensional system to have an integral manifold are given. Especially the existence and uniqueness of a 3-dimensional invariant torus appearing in a 4-dimensional autonomous system with singularity of codimension two are proved.
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| 收稿时间： | 14 July 2004 |
Existence and bifurcation of integral manifolds with applications |
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| HAN Mao''''an & CHEN Xianfeng.Existence and bifurcation of integral manifolds with applications[J].Science in China(Mathematics),2005,48(7):940-957. |
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| Authors: | HAN Mao'an Chen Xianfeng |
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| Institution: | 1. Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200030, China |
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| Abstract: | In this paper a bifurcation theorem on the existence of integral manifolds is obtained by using contracting principle. As an application, sufficient conditions for a higher dimensional system to have an integral manifold are given. Especially the existence and uniqueness of a 3-dimensional invariant torus appearing in a 4-dimensional autonomous system with singularity of codimension two are proved. |
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| Keywords: | existence bifurcation invariant manifold invariant torus |
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