具有非Morsean点的二次可逆系统(r6)的极限环分支

隋世友, 徐伟骄

数学学报 ›› 2021, Vol. 64 ›› Issue (6) : 999-1004.

PDF(383 KB)
PDF(383 KB)
数学学报 ›› 2021, Vol. 64 ›› Issue (6) : 999-1004. DOI: 10.12386/A2021sxxb0083
论文

具有非Morsean点的二次可逆系统(r6)的极限环分支

    隋世友, 徐伟骄
作者信息 +

Bifurcation of Limit Cycles from the Center of Quadratic Reversible System (r6) with non-Morsean Point

    Shi You SUI, Wei Jiao XU
Author information +
文章历史 +

摘要

本文考虑了具有非Morsean点的二次可逆系统(r6)在二次多项式扰动下可分支出的极限环的个数.证明了可分支出极限环个数的上确界是2,验证了[Iliev I.D.,Perturbations of quadratic centers,Bull.Sci.Math.,1998,122:107-161]的猜测.

Abstract

We consider the number of limit cycles bifurcating from the center of quadratic reversible system (r6) with non-Morsean point under quadratic perturbations. It is proved that the sharper bound is 2, which verifies the conjecture given by[Iliev I. D., Perturbations of quadratic centers, Bull. Sci. Math., 1998, 122:107-161].

关键词

极限环 / Abel积分 / 广义完备Chebyshev系统

Key words

limit cycle / Abelian integral / extended complete Chebyshev system

引用本文

导出引用
隋世友, 徐伟骄. 具有非Morsean点的二次可逆系统(r6)的极限环分支. 数学学报, 2021, 64(6): 999-1004 https://doi.org/10.12386/A2021sxxb0083
Shi You SUI, Wei Jiao XU. Bifurcation of Limit Cycles from the Center of Quadratic Reversible System (r6) with non-Morsean Point. Acta Mathematica Sinica, Chinese Series, 2021, 64(6): 999-1004 https://doi.org/10.12386/A2021sxxb0083

参考文献

[1] Artés J. C., Llibre J., Schlomiuk D., The geometry of quadratic differential systems with a weak focus of second order, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 2006, 16:3127-3194.
[2] Chen F. D., Li C. Z., Llibre J., et al., A unified proof on the weak Hilbert 16th problem for n=2, J. Differ. Equ., 2006, 221:309-342.
[3] Chen G. T., Li C. Z., Liu C. J., et al., The cyclicity of period annuli of some classes of reversible quadratic systems, Discrete Contin. Dyn. Syst., 2006, 16:157-177.
[4] Gautier S., Gavrilov L., Iliev I. D., Perturbations of quadratic centers of genus one, Discrete Contin. Dyn. Syst., 2009, 25:511-535.
[5] Gavrilov L., The infinitesima 16th Hilbert problem in the quadratic case, Invent. Math., 2001, 143:449-497.
[6] Grau M., Mañosas F., Villadelprat J., A Chebyshev criterion for Abelian integrals, Trans. Amer. Math. Soc., 2011, 363:109-129.
[7] Iliev I. D., Perturbations of quadratic centers, Bull. Sci. Math., 1998, 122:107-161.
[8] Karlin S., Studden W. J., Tchebycheff Systems:With Applications in Analysis and Statistics, Pure and Applied Mathematics, Vol. XV, Interscience Publishers John Wiley & Sons, New York, 1966.
[9] Li C. Z., Li W. G., Weak Hilbert's 16th problem and the related research (in Chinese), Adv. Math., 2010, 39:513-526.
[10] Li C. Z., Zhang Z. H., Remarks on 16th weak Hilbert problem for n=2, Nonlinearity, 2002, 15:1975-1992.
[11] Pontryagin L., On dynamical systems close to Hamiltonian ones, Zh. Exp. Theor. Phys., 1934, 4:234-238.
[12] Zhao Y. L., On the number of limit cycles in quadratic perturbations of quadratic codimension four centers, Nonlinearity, 2011, 24:2505-2522.
[13] Zhao Y. L., Chen Y. Y., The cyclicity of quadratic reversible systems with a center of genus one and nonMorsean point, Appl. Math. Comput., 2014, 231:268-275.
[14] Zoladek H., Quadratic systems with center and their perturbations,·J. Differ. Equ., 1994, 109:223-273.

基金

国家自然科学基金资助项目(11801414)
PDF(383 KB)

Accesses

Citation

Detail

段落导航
相关文章

/