一类Liénard系统的零点个数最小上界研究
A Study on the Upper Number of Zeros for a Liénard System
DOI: 10.12677/PM.2021.117162, PDF,   
作者: 李成群, 胡雪婷, 韦敏志*：广西财经学院信息与统计学院，广西 南宁
关键词: Liénard系统；Abel积分；同宿轨；零点个数；Liénard System； Abel Integral； Homoclinic Orbit； The Number of Zeros
摘要: 本文运用Abel积分生成元的切比雪夫理论结合多项式符号计算技术，对(4, 3)型的Liénard系统对应的Abel积分的零点个数上界进行研究分析。求出I(h,δ)的零点个数的最小上界。讨论以下系统 Abel积分的零点个数问题。通过对其Abel积分I(h,δ)的深入研究，证明阿贝尔积分的生成元能否构成Chebeyshev系统，得出其零点个数的上界。
Abstract: In this paper, we aim to use Chebyshev theory of Abel integral generator and polynomial symbolic computing technology to study and analyze the upper bound of the number of zeros of Abel integral corresponding to (4, 3) Liénard system. The minimum upper bound of the number of zeros for I(h,δ) is proved. The number of zeros of Abel integral of following Liénard system is considered . Through the in-depth study of Abel integral I(h,δ), it is proved that the generator of Abel integral can form Chebeyshev system, and a conclu-sion is shown.
文章引用：李成群, 胡雪婷, 韦敏志. 一类Liénard系统的零点个数最小上界研究[J]. 理论数学, 2021, 11(7): 1441-1450. https://doi.org/10.12677/PM.2021.117162

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