Limit Cycles Near a Centre and a Heteroclinic Loop in a Near–Hamiltonian Differential System
Limit Cycles Near a Centre and a Heteroclinic Loop in a Near–Hamiltonian Differential System
复制标题
近哈密尔顿微分系统中中心附近的极限环和异斜环
DOI：
10.1007/s10884-022-10152-3
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发表时间：
2022
影响因子：
1.3
通讯作者：
Jinbo Zhu
中科院分区：
文献类型：
--
作者：
Lijun Wei;Xiang Zhang;Jinbo Zhu
This paper studies limit cycle bifurcation of anth order generalized Liénard differential system with an elliptic Hamiltonian, which bifurcates at leastlimit cycles near either a centre or a heteroclinic loop with two hyperbolic saddles for, where about two thirds of the limit cycles are large amplitude ones. To achieve this goal, we provide the precise expression of the third coefficient in the asymptotic expansion of the first order Melnikov function of an analytic near-Hamiltonian system near a polycycle withhyperbolic saddles, without any prescribed condition, whereas all the known results need. As well as we also characterize its higher order coefficients. Here [a] is the integer part function of a real numbera.
