Abelian Integrals and Limit Cycles

被引：52
作者：
Li, Chengzhi [1 ]
机构：
[1] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
来源：
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2012年 / 11卷 / 01期
关键词：
Abelian integral; Limit cycle; Weak Hilbert's 16th problem; QUADRATIC REVERSIBLE-SYSTEMS; PERIOD ANNULUS; HILBERT PROBLEM; HAMILTONIAN-SYSTEMS; 16TH PROBLEM; CENTERS; PERTURBATIONS; NUMBER; CYCLICITY; ZEROS;
D O I：
10.1007/s12346-011-0051-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This survey paper is devoted to introducing some basic concepts and methods about the application of Abelian integral to study the number of limit cycles, especially to the weak Hilbert's 16th problem. We will introduce some recent results in this field.
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收藏
页码：111 / 128
页数：18
相关论文
共 91 条
[1]  
[Anonymous], 2008, LECT ANAL DIFFERENTI
[2]  
[Anonymous], 2010, Qual. Theo. Dyna. Syst., DOI DOI 10.1007/S12346-010-0024-7)
[3]  
Arnold V.I., 1990, Adv. Soviet Math, V1, P1
[4]  
Arnold VI, 1977, Funct Anal Appl, V11, P85, DOI [10.1007/BF01081886, DOI 10.1007/BF01081886]
[5]  
Binyamini G, 2010, INVENT MATH, V181, P227, DOI 10.1007/s00222-010-0244-0
[6]   Alien limit cycles near a Hamiltonian 2-saddle cycle [J].
Caubergh, M ;
Dumortier, F ;
Roussarie, R .
COMPTES RENDUS MATHEMATIQUE, 2005, 340 (08) :587-592
[7]   Hopf-takens bifurcations and centres [J].
Caubergh, M ;
Dumortier, F .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 202 (01) :1-31
[8]   A unified proof on the weak Hilbert 16th problem for n=2 [J].
Chen, F ;
Li, CZ ;
Llibre, J ;
Zhang, ZH .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 221 (02) :309-342
[9]  
Chen G, 2006, DISCRETE CONT DYN-A, V16, P157
[10]  
Chen L., J APPL ANAL IN PRESS
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