THE NUMBER OF LIMIT CYCLES FROM ELLIPTIC HAMILTONIAN VECTOR FIELDS BY HIGHER ORDER MELNIKOV FUNCTIONS

被引：0
|
作者：
Liu, Xia [1 ]
机构：
[1] Zhongyuan Univ Technol, Colleof Sci, Zhengzhou 450007, Peoples R China
来源：
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2023年 / 13卷 / 03期
关键词：
Melnikov functions; bifurcation; limit cycles; generators; POLYNOMIAL PERTURBATIONS; BIFURCATIONS; ANNULUS; HOPF;
D O I：
10.11948/20220063
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the perturbed Hamiltonian system dH = 6F4 + 62F3 + 63F2 + 64F1, with Fi the vector valued homogeneous polynomials of degree i. The Hamiltonian function is H = y2/2 + U(X), where U is a uni-variate polynomial of degree four without symmetry. By computing higher order Melnikov functions, the upper bounds for the number of limit cycles that bifurcate from dH = 0 are deserved.
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页码：1239 / 1254
页数：16
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