Quadratic perturbations of a quadratic reversible center of genus one

被引：1
|
作者：
Peng, Linping [1 ]
机构：
[1] Beijing Univ Aeronaut & Astronaut, Sch Math & Syst Sci, LIMB, Minist Educ, Beijing 100191, Peoples R China
来源：
FRONTIERS OF MATHEMATICS IN CHINA | 2011年 / 6卷 / 05期
基金：
中国国家自然科学基金;
关键词：
Quadratic reversible and non-Hamiltonian system; genus one; period annulus; limit cycle; cyclicity; LIMIT-CYCLES; HAMILTONIAN-SYSTEMS; HILBERT PROBLEM; PERIOD ANNULI; BIFURCATIONS; CYCLICITY;
D O I：
10.1007/s11464-011-0155-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study a reversible and non-Hamitonian system with a period annulus bounded by a hemicycle in the Poincar, disk. It is proved that the cyclicity of the period annulus under quadratic perturbations is equal to two. This verifies some results of the conjecture given by Gautier et al.
引用
收藏
页码：911 / 930
页数：20
相关论文
共 50 条
  • [1] Quadratic perturbations of a quadratic reversible center of genus one
    Linping Peng
    Frontiers of Mathematics in China, 2011, 6 : 911 - 930
  • [2] QUADRATIC PERTURBATIONS OF A CLASS OF QUADRATIC REVERSIBLE SYSTEMS WITH ONE CENTER
    Liang, Haihua
    Zhao, Yulin
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2010, 27 (01) : 325 - 335
  • [3] Quadratic perturbations of a class of quadratic reversible center of genus one
    Liang HaiHua
    Wu KuiLin
    Zhao YuLin
    SCIENCE CHINA-MATHEMATICS, 2013, 56 (03) : 577 - 596
  • [4] The cyclicity of the period annulus of a quadratic reversible system with one center of genus one
    Peng, Linping
    Sun, Yannan
    TURKISH JOURNAL OF MATHEMATICS, 2011, 35 (04) : 667 - 685
  • [5] On the Limit Cycles Bifurcating from a Quadratic Reversible Center of Genus One
    Peng, Linping
    Li, You
    MEDITERRANEAN JOURNAL OF MATHEMATICS, 2014, 11 (02) : 373 - 392
  • [6] Quadratic perturbations of a class of quadratic reversible center of genus one
    HaiHua Liang
    KuiLin Wu
    YuLin Zhao
    Science China Mathematics, 2013, 56 : 577 - 596
  • [7] Quadratic perturbations of a class of quadratic reversible center of genus one
    LIANG HaiHua
    WU KuiLin
    ZHAO YuLin
    Science China(Mathematics), 2013, 56 (03) : 577 - 596
  • [8] PERTURBATIONS OF QUADRATIC CENTERS OF GENUS ONE
    Gautier, Sebastien
    Gavrilov, Lubomir
    Iliev, Iliya D.
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 25 (02) : 511 - 535
  • [9] A class of quadratic reversible systems with a center of genus one
    Xiong, Yanqin
    Zhang, Tonghua
    CHAOS SOLITONS & FRACTALS, 2018, 114 : 119 - 129
  • [10] Limit cycles bifurcated from a class of quadratic reversible center of genus one
    Liang, Haihua
    Zhao, Yulin
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 391 (01) : 240 - 254
12345