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On the Melnikov functions and limit cycles near a double homoclinic loop with a nilpotent saddle of order mˆ
Journal of Differential Equations ( IF 2.4 ) Pub Date : 2021-05-10 , DOI: 10.1016/j.jde.2021.04.032
Junmin Yang , Pei Yu , Maoan Han

For a centrally symmetric near-Hamiltonian system, we develop a method for computing all the coefficients in the expansions of three Melnikov functions near a double homoclinic loop. Moreover, we give a new estimation on the lower bound of H(2nˆ,5) for 11nˆ23, where H(2nˆ,5) is the maximal number of limit cycles for a kind of Liénard system, x˙=y,y˙=g(x)+εf(x)y, with degg(x)=5 and degf(x)=2nˆ.



中文翻译:

关于Melnikov函数和极限环,它具有阶幂幂鞍的双同宿环附近 ˆ

对于中心对称的近哈密顿系统,我们开发了一种计算双均斜环附近三个Melnikov函数展开式中所有系数的方法。此外,我们对H2个ñˆ5 为了 11ñˆ23, 在哪里 H2个ñˆ5 是一种Liénard系统的最大极限环数, X˙=ÿÿ˙=-GX+εFXÿ, 和 GX=5FX=2个ñˆ

更新日期:2021-05-10
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