Quadratic perturbations of a quadratic reversible center of genus one

被引：0
作者：
Linping Peng
机构：
[1] Beijing University of Aeronautics and Astronautics,School of Mathematics and System Sciences
[2] LIMB of the Ministry of Education,undefined
来源：
Frontiers of Mathematics in China | 2011年 / 6卷
关键词：
Quadratic reversible and non-Hamiltonian system; genus one; period annulus; limit cycle; cyclicity; 34C07; 34C08; 37G15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we study a reversible and non-Hamitonian system with a period annulus bounded by a hemicycle in the Poincaré 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：19
相关论文
共 45 条
[1]  
Chen F.(2006)A unified proof on the weak Hilbert 16th problem for J Differ Equations 221 309-342
[2]  
Li C.(2006) = 2 Discrete Cont Dyn S 16 157-177
[3]  
Liu C.(1991)The cyclicity of period annuli of some classes of reversible quadratic systems J Differ Equations 91 268-326
[4]  
Llibre J.(2002)Bifurcation of limit cycles from quadratic isochrones Ergod Theor Dyn Syst 22 349-374
[5]  
Chen G.(2009)The cyclicity of period annulus of degenerate quadratic Hamiltonian system with elliptic segment loops Discrete Cont Dyn S 24 699-729
[6]  
Li C.(1997)Quadratic perturbations of a class of quadratic reversible systems with two centers J Differ Equations 139 146-193
[7]  
Liu C.(2009)Unfolding of a quadratic integrable system with two centers and two unbounded heteroclinic loops Discrete Cont Dyn S 25 511-535
[8]  
Llibre J.(2001)Perturbations of quadratic center of genus one Invent Math 143 449-497
[9]  
Chicone C.(1994)The infinitesimal 16th Hilbert problem in the quadratic case Proc London Math Soc 69 198-224
[10]  
Jacobs M.(1998)On the number of limit cycles in perturbations of quadratic Hamiltonian system Bull Sci Math 122 107-161
12345