| Bifurcation of limit cycles near equivariant compound cycles |
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| 作者姓名： | Mao-an HAN Tong-hua ZHANG & Hong ZANG |
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| 作者单位： | Mao-an HAN，Tong-hua ZHANG & Hong ZANG Department of Mathematics，Shanghai Normal University，Shanghai 200234，China |
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| 基金项目： | 国家自然科学基金;教育部高校新世纪杰出人才项目 |
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| 摘 要： | In this paper we study some equivariant systems on the plane. We first give some criteria for the outer or inner stability of compound cycles of these systems. Then we investigate the number of limit cycles which appear near a compound cycle of a Hamiltonian equivariant system under equivariant perturbations. In the last part of the paper we present an application of our general theory to show that a Z3 equivariant system can have 13 limit cycles.
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| 收稿时间： | 3 May 2005 |
| 修稿时间： | 14 July 2006 |
Bifurcation of limit cycles near equivariant compound cycles |
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| Mao-an HAN,Tong-hua ZHANG & Hong ZANG.Bifurcation of limit cycles near equivariant compound cycles[J].Science in China(Mathematics),2007,50(4):503-514. |
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| Authors: | Mao-an Han Tong-hua Zhang Hong Zang |
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| Institution: | Department of Mathematics,Shanghai Normal University,Shanghai 200234,China |
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| Abstract: | In this paper we study some equivariant systems on the plane. We first give some criteria for the outer or inner stability of compound cycles of these systems. Then we investigate the number of limit cycles which appear near a compound cycle of a Hamiltonian equivariant system under equivariant perturbations. In the last part of the paper we present an application of our general theory to show that a Z3 equivariant system can have 13 limit cycles. |
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| Keywords: | equivariant system stability bifurcation limit cycle |
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