一类扰动的二次可逆系统的Abel 积分的上界估计
Upper Bound Estimation of AbelianIntegral for a Class of PerturbedQuadratic Reversible Systems
DOI: 10.12677/PM.2023.136193, PDF, HTML, 下载: 211  浏览: 287  科研立项经费支持
作者: 占园根*, 杨利华：景德镇陶瓷大学信息工程学院，江西 景德镇；朱丽云：浮梁县南安中学，江西 景德镇
关键词: 二次可逆系统；Abel积分；极限环；Riccati方程；Quadratic Reversible Systems； Abelian Integral； Limit Cycles； Riccati Equation
摘要: 利用Riccati方程法，研究了一类亏格1形式的二次可逆系统(r9)在任意3, 2, 1次多项式扰动下的Abel积分孤立零点个数的上界。 得到的结果为: 在3, 2, 1次多项式扰动下上界是13。 这些结果是 对之前结果的改进。
Abstract: By using Riccati equation method, the upper bound estimation of the number of zeros of Abelian integral for a class of quadratic reversible system (r9) of genus one under any polynomial perturbation of degree 3; 2; 1 is studied. The result is that the upper bound is 13 under polynomial perturbation of degree 3; 2; 1. These results are an improvement of the previous results.
文章引用：占园根, 杨利华, 朱丽云. 一类扰动的二次可逆系统的Abel 积分的上界估计[J]. 理论数学, 2023, 13(6): 1888-1896. https://doi.org/10.12677/PM.2023.136193

参考文献

[1] 李承治, 李伟固. 弱化希尔伯特第16问题及其研究现状[J]. 数学进展, 2010, 39(5): 513-526.
[2] Han, M. (2013) Bifurcation Theory of Limit Cycles. Science Press, Beijing, 310-312.
[3] 赵育林. 三次Hamilton向量场的Abel积分[D]: [博士学位论文]. 北京: 北京大学, 1998.
[4] Li, J. (2003) Hilbert's 16th Problem and Bifurcations of Planar Polynomial Vector Fields. International Journal of Bifurcation and Chaos, 13, 47-106.
https://doi.org/10.1142/S0218127403006352
[5] Horozov, E. and Iliev, I.D. (1998) Linear Estimate for the Number of Zeros of Abelian Integrals with Cubic Hamiltonians. Nonlinearity, 11, 1521-1537.
https://doi.org/10.1088/0951-7715/11/6/006
[6] Gautier, S., Gavrilov, L. and Iliev, I.D. (2009) Perturbations of Quadratic Centers of Genus One. Discrete and Continuous Dynamical Systems, 25, 511-535.
https://doi.org/10.3934/dcds.2009.25.511
[7] Zhao, Y., Li, W., Li, C. and Zhang, Z. (2002) Linear Estimate of the Number of Zeros of Abelian Integrals for Quadratic Centers Having Almost All Their Orbits Formed by Cubics. Science in China, Series A: Mathematics, 45, 964-974.
https://doi.org/10.1007/BF02879979
[8] Li, W., Zhao, Y., Li, C. and Zhang, Z. (2002) Abelian Integrals for Quadratic Centres Having Almost All Their Orbits Formed by Quartics. Nonlinearity, 15, 863-885.
https://doi.org/10.1088/0951-7715/15/3/321
[9] Hong, X., Xie, S. and Chen, L. (2016) Estimating the Number of Zeros for Abelian Integrals of Quadratic Reversible Centers with Orbits Formed by Higher-Order Curves. International Journal of Bifurcation and Chaos, 26, Article ID: 1650020.
https://doi.org/10.1142/S0218127416500206
[10] Hong, X., Xie, S. and Ma, R. (2015) On the Abelian Integrals of Quadratic Reversible Centers with Orbits Formed by Genus One Curves of Higher Degree. Journal of Mathematical Analysis and Applications, 429, 924-941.
https://doi.org/10.1016/j.jmaa.2015.03.068
[11] Hong, X., Lu, J. and Wang, Y. (2018) Upper Bounds for the Associated Number of Zeros of Abelian Integrals for Two Classes of Quadratic Reversible Centers of Genus One. Journal of Applied Analysis and Computation, 8, 1959-1970.
https://doi.org/10.11948/2018.1959
[12] Hong, L., Lu, J. and Hong, X. (2020) On the Number of Zeros of Abelian Integrals for a Class of Quadratic Reversible Centers of Genus One. Journal of Nonlinear Modeling and Analysis, 2, 161-171.
[13] Hong, L., Hong, X. and Lu, J. (2020) A Linear Estimation to the Number of Zeros for Abelian Integrals in a Kind of Quadratic Reversible Centers of Genus One. Journal of Applied Analysis and Computation, 10, 1534-1544.
https://doi.org/10.11948/20190247

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