Higher Order Melnikov Functions for Studying Limit Cycles of Some Perturbed Elliptic Hamiltonian Vector Fields

被引：4

作者：

Asheghi, Rasoul ^{[1
]}

Nabavi, Arefeh ^{[1
]}

机构：

[1] Isfahan Univ Technol, Dept Math Sci, Esfahan 8415683111, Iran

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2019年 / 18卷 / 01期

关键词：

Limit cycles; Hamiltonian systems; Melnikov functions;

D O I：

10.1007/s12346-018-0284-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the number of limit cycles in the perturbed Hamiltonian system dH=epsilon F1+epsilon 2F2+epsilon 3F3 with Fi, the vector valued homogeneous polynomials of degree i and 4-i for i=1,2,3, and small positive parameter epsilon. The Hamiltonian function has the form H=y2/2+U(x), where U is a univariate polynomial of degree four without symmetry. We compute higher order Melnikov functions until we obtain reversible perturbations. Then we find the upper bounds for the number of limit cycles that can bifurcate from the periodic orbits of dH=0.

引用

页码：289 / 313

页数：25

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