[1]李慧敏,张二丽*.具幂零鞍点的Hamilton系统的周期环域的环性[J].四川师范大学学报(自然科学版),2019,(05):598-604.[doi:10.3969/j.issn.1001-8395.2019.05.005]
 LI Huimin,ZHANG Erli.The Cyclicity of Period Annuli of a Hamilton System with Nilpotent Saddle Points[J].Journal of SichuanNormal University,2019,(05):598-604.[doi:10.3969/j.issn.1001-8395.2019.05.005]
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具幂零鞍点的Hamilton系统的周期环域的环性()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2019年05期
页码:
598-604
栏目:
基础理论
出版日期:
2019-07-15

文章信息/Info

Title:
The Cyclicity of Period Annuli of a Hamilton System with Nilpotent Saddle Points
文章编号:
1001-8395(2019)05-0598-07
作者:
李慧敏 张二丽*
郑州财经学院 信息工程学院, 河南 郑州 450001
Author(s):
LI Huimin ZHANG Erli
School of Information Engineering, Zhengzhou Institute of Finance and Economics, Zhengzhou 450001, Henan
关键词:
Melnikov函数 周期环域 弱Hilbert 16问题 Picard-Fuchs方程
Keywords:
Melnikov function period annuli Weakened Hilbert's 16th Problem Picard-Fuchs equation
分类号:
O175.12
DOI:
10.3969/j.issn.1001-8395.2019.05.005
文献标志码:
A
摘要:
研究具有幂零鞍点的三次Hamilton系统(dx)/(dt)=4x2y+4y3-y,(dy)/(dt)=4x3-4xy2+x的周期环域的环性.应用一阶Melnikov函数和Picard-Fuchs方程,得到该系统在n次实多项式扰动下从其周期环域中最多分支出4n+10个极限环(计重数).
Abstract:
In this paper, we study the cyclicity of period annuli of the following cubic Hamilton system with nilpotent saddle points(dx)/(dt)=4x2y+4y3-y,(dy)/(dt)=4x3-4xy2+x.By using the first order Melnikov function and Picard-Fuchs equation, we obtain that the above system under perturbations of real polynomials with degree n can bifurcate at most 4n+10 limit cycles(taking into account the multiplicity).

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备注/Memo

备注/Memo:
收稿日期:2018-01-21 接受日期:2018-09-25
基金项目: 国家自然科学基金(11701306)、河南省高等学校重点科研项目(19A110033和19B11001)和河南省高等学校青年骨干教师培养计划(2017GGJS202和2016GGJS190)
*通信作者简介:张二丽(1983—),女,副教授,主要从事微分方程的稳定性与分支理论的研究,E-mail:isszel@163.com
更新日期/Last Update: 2019-07-15