论文标题
限制周期从具有基本马鞍的广义杂斜环出现，并通过扰动分段哈密顿系统的nilpotent鞍座
Limit Cycles Appearing from a Generalized Heteroclinic Loop with an Elementary Saddle and a Nilpotent Saddle by Perturbing Piecewise Hamiltonian Systems
论文作者
论文摘要
在本文中，我们研究了一类杂斜环和带有基本马鞍和nilpotent鞍座的一类近木尔顿系统的限制周期分叉。首先，我们考虑了不受干扰的系统的行为，提供了系统的相位肖像以及使用相关定性理论的基本马鞍和nilpotent鞍形出现杂斜环的必要条件。然后，考虑到一阶Melnikov函数的表达，我们通过采用Abelian积分的某些技术和特性来得出其在杂斜环附近的膨胀。最后，我们研究了扩展的系数，并表明至少存在$ 4 [\ frac {n+1} {2}]+1 $限制在干扰下的限制周期。
In this paper, we study limit cycle bifurcations for a class of general near-Hamiltonian systems near a heteroclinic loop with an elementary saddle and a nilpotent saddle. Firstly, we consider the behaviors of the unperturbed system, providing the phase portraits of the system and the necessary conditions for the appearance of a heteroclinic loop with an elementary saddle and a nilpotent saddle by using the relevant qualitative theory. Then, with consideration of the expression of the first-order Melnikov function, we derive its expansion near the heteroclinic loop by employing some techniques and properties of the Abelian integral. Finally, we investigate the coefficients of the expansion and show that there can exist at least $4[\frac{n+1}{2}]+1$ limit cycles under disturbance.
