| 关于Birkhoff系统的周期解 |
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| 引用本文： | 洪友诚,尹群.关于Birkhoff系统的周期解[J].南京理工大学学报(自然科学版),1996,20(1):75-78. |
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| 作者姓名： | 洪友诚 尹群 |
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| 作者单位： | 南京理工大学理学院 |
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| 摘 要： | 该文利用广义导引函数方法证明了Ｂｉｒｋｈｏｆｆ系统存在Ｔ周期解，其中ε是小参数，Ω１可逆，Ω２（ｘ）在Ｒ２ｎ上有界，Ｂ１反对称，Ｂ２（ｔ，ｘ）关于ｔ是Ｔ周期的，关于Ｘ在远离ｘ＝０处亚二次且的本征值都有非零实部。对上述系统的自治情形用分歧方法证明了在平衡态附近有在给定的等量面上的周期解，其中可逆，Ｂ１负定，Ω２（ｘ）和Ｂ２（ｘ）在ｘ＝０附近超二次。
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| 关 键 词： | Birkhoff系统 周期解 广义导引函数 分歧 |
On the Periodic Solutions of Birkhoffian Systems |
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| Hong Youcheng,Yin Qun.On the Periodic Solutions of Birkhoffian Systems[J].Journal of Nanjing University of Science and Technology(Nature Science),1996,20(1):75-78. |
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| Authors: | Hong Youcheng Yin Qun |
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| Abstract: | In the first part of this paper,we prove the existence of T periodic solutions for Birkhoffian systems,where,is a small parameterl,is an invertible matrixl is bounded onn R2n;B1 is a skew symmetric matrix;B_2(t,x) is T periodic in t and is subquadratie in x with |x| large;and the eigenvalues of,have all non-zero real part.In the second part,we prove the existence of periodic solutions on prescribed equiscalar surface,near equilibrium by bifurcation method for autonomous case of the above systems with where is an invertible matric;B_1 is a negative definite matric,(x) and B2(x) are superquadratic near x=0. |
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| Keywords: | Birkhoffian systems periodic solutions generalized guiding functions bifurcation |
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