具有高阶扰动的二维拟周期系统的约化性
Reducibility for Two Dimensional Quasi-Periodic System with High Order Perturbations
孟凡卉 1邱汶华1
作者信息
- 1. 枣庄学院 数学与统计学院,山东 枣庄 277160
- 折叠
摘要
通过寻找合适的拟周期变换,把高阶扰动二维拟周期系统变成简单的正规形.寻找拟周期变换序列,求解拟周期变换导出的同调方程,确定变换的具体形式;利用Diophantine条件克服变换时出现的小除数问题,进行范数估计;求变换序列的极限,得到原系统的约化性结果.用KAM中的迭代方法和 5 次多项式扰动的相关结论证明了相关定理.
Abstract
The two dimensional quasi-periodic system with high order perturbations is transformed into a simple normal form by finding a suitable quasi-periodic transformation.The sequence of quasi-periodic transformation is found,and the homology e-quation derived from the quasi-periodic transformation is solved to determine the concrete form of the transformation The Dio-phantine condition is used to solve the small divisor problem in the transformation,and the norm is estimated.The transforma-tion limit of the sequence is obtained,and the reduction result of the original system is obtained.The iterative method in KAM and the related results of 5-degree polynomial perturbation are used in the proof of the theorem.
关键词
拟周期解/KAM理论/高阶扰动Key words
quasi-periodic solution/KAM theorem/high order perturbation引用本文复制引用
基金项目
国家自然科学基金面上项目(12171420)
教育部产学合作协同育人项目(220901503221020)
出版年
2024
NETL
NSTL
万方数据