| E1ementary Bifurcations of Non—Critical but N0n—Hyperbolic Invariant Tori |
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| 作者姓名： | JianHuaSUN |
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| 作者单位： | DepartmentofMathemnatics,NanjingUniversity,Nanjing210008 |
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| 摘 要： | Consider the time-periodic peturbations of n-dimensional autonomous systems with non-hyperbolic but non-critical closed orbits in the phase space.The elementary bifurcations,such as the saddle-node,transcritical,pitchfork bifurcation to a non-hyperbolic but non-critical invariant torus of the unperturbed systems in the extended phase space(x,t),are sutdied.Some conditions which depend only on ithe original systems and can be used to determine the bifurcation structures of these problems are obtained.The theory is applied to two concrete examples.
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| 关 键 词： | 非双曲非临界不变环面 环面 周期扰动 初等分歧 平均方法 李雅普诺夫－施密特方法 |
| 收稿时间： | 22 February 2000 |
Elementary Bifurcations of Non-Critical but Non-Hyperbolic Invariant Tori |
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| JianHuaSUN.Elementary Bifurcations of Non-Critical but Non-Hyperbolic Invariant Tori[J].Acta Mathematica Sinica,2003,19(1):159-170. |
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| Authors: | Email author" target="_blank">Jian?Hua?SunEmail author |
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| Institution: | (1) Department of Mathematics, Nanjing University, Nanjing 210008, P. R. China |
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| Abstract: | Consider the time-periodic perturbations of n-dimensional autonomous systems with nonhyperbolic but non-critical closed orbits in the phase space. The elementary bifurcations,
such as the saddle-node, transcritical, pitchfork bifurcation to a non-hyperbolic but non-critical invariant torus of the
unperturbed systems in the extended phase space (x, t), are studied. Some conditions which depend only on the original systems and can be used to determine the bifurcation structures
of these problems are obtained. The theory is applied to two concrete examples.
Project supported by the National Natural Science Foundation of China (No. 10171044) and the Foundation for University Key
Teachers by the Ministry of Education |
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| Keywords: | Nonhyperbolic but noncritical invariant tori Periodic perturbation Elementary bifurcation Scaling Averaging method Lyapunov-Schmidt method |
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