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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
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
更新日期:2021-05-10
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 for , where is the maximal number of limit cycles for a kind of Liénard system, , with and .
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
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 为了 , 在哪里 是一种Liénard系统的最大极限环数, , 和 和 。