| Periodic Orbits and Invariant Tori from a Semistable Limit Cycle in the Fast Dynamics |
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| 作者姓名： | 叶志勇 韩茂安 |
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| 作者单位： | Dept.of Mathematics Shanghai Jiaotong Univ.，Shanghai 200240 China，Dept. of Mathematics，Chongqing Inst.of Technology Chongqing 400050，Dept.of Mathematics Shanghai Jiaotong Univ.，Shanghai 200240 China |
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| 基金项目： | NationalNaturalScienceFoundationofChina(No.10371138,No.10371072)andEduca-tionCommissionofChongqing,China |
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| 摘 要： | IntroductionIn the paper,the bifurcations of periodic or-bits and invariant tori of the following system wasstudied:x。=f(x,y) εh(t,x,y,ε)∈R2y。=εg(t,x,y,ε)∈R,0≤ε1(1)where h(t,x,y,ε)and g(t,x,y,ε)are T-periodicin t.For simplicity,the functions f,g and h areassumed to be sufficiently smooth in their argu-ments throughout this paper.In Ref.1],Wiggins and Holmes called thesystems of form Eq.(1)as slowly varying oscilla-tors and pointed out that the systems taking theform occur as mo…
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| 文章编号： | 1007-1172（2006）01-0107-06 |
| 收稿时间： | 2005-04-01 |
Periodic Orbits and Invariant Tori from a Semistable Limit Cycle in the Fast Dynamics |
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| YE Zhi-yong,HAN Mao-an.Periodic Orbits and Invariant Tori from a Semistable Limit Cycle in the Fast Dynamics[J].Journal of Shanghai Jiaotong university,2006,11(1):107-112. |
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| Authors: | YE Zhi-yong HAN Mao-an |
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| Abstract: | Some global behavior for a slowly varying oscillator was investigated. Based on a series of transformations and the theory of periodic orbits and integral manifold, the bifurcations of subharmonic solutions and invariant tori generated from a semistable limit cycle in the fast dynamics were discussed. |
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| Keywords: | singular perturbation subharmonic solution invariant torus |
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