一类常见摆方程的摄动问题
Perturbation Problems for a Class of Common Pendulum Equations
DOI: 10.12677/PM.2021.1112219, PDF,    国家自然科学基金支持
作者: 孟凡卉, 邱汶华*：枣庄学院数学与统计学院，山东 枣庄
关键词: 摆方程；迭代法；可约化性；Pendulum Equation； Iterative Method； Reducibility
摘要: 本文主要研究了一类常见摆方程的摄动问题。该摆方程不同于经典的摆方程。本文研究了此类方程带扰动形式的可约化性。借助于KAM迭代法的思想，通过无穷次迭代，可以将方程约化为系数为常数的形式。
Abstract: This paper focuses on perturbation problems for a class of common pendulum equations. The pendulum equations are different from classical pendulum equations. We study the reducibility of the perturbed form for such equations. With the thought of KAM iterative method, the equation can be reduced to a suitable form, and the coefficient will be reduced to constant by infinite iterations.
文章引用：孟凡卉, 邱汶华. 一类常见摆方程的摄动问题[J]. 理论数学, 2021, 11(12): 1967-1973. https://doi.org/10.12677/PM.2021.1112219

参考文献

[1] 张子方, 蒋建军, 傅英贵, 林军, 苏英. 一类摆动方程概周期解的存在性[J]. 浙江大学学报(理学版), 2001, 28(4): 360-363.
[2] Jorba, A. and Simo, C. (1996) On Quasi-Periodic Perturbations of Elliptic Equilibrium Points. SIAM Journal on Mathematical Analysis, 27, 1704-1737. [Google Scholar] [CrossRef] 
[3] Xu, J. (2007) Persistence of Floquet Invariant Tori for a Class of Non-Conservative Dynamical Systems. Proceedings of the American Mathematical Society, 135, 805-814. [Google Scholar] [CrossRef] 
[4] Geng, J. and Wu, J. (2017) Real Analytic Quasi-Periodic Solutions with More Diophantine Frequencies for Perturbed KdV Equations. Journal of Dynamics and Differential Equations, 29, 1103-1130. [Google Scholar] [CrossRef] 
[5] Her, H. and You, J. (2008) Full Measure Reducibility for Generic One-Parameter Family of Quasi-Periodic Linear Systems. Journal of Dynamics and Differential Equations, 20, 831-866. [Google Scholar] [CrossRef] 
[6] Qiu, W.H. and Si, J.G. (2015) On Small Perturbation of Four-Dimensional Quasi-Periodic Systems with Degenerate Equilibrium Point. Communications on Pure and Applied Analysis, 14, 421-437. [Google Scholar] [CrossRef] 
[7] Xu, J.X. (2011) On Small Perturbation of Two-Dimensional Qua-si-Periodic Systems with Hyperbolic-Type Degenerate Equilibrium Point. Journal of Differential Equations, 250, 551-571. [Google Scholar] [CrossRef] 

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