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引用次数: 0
摘要
本文介绍了一个抽象的 KAM（Kolmogorov-Arnold-Moser）定理。作为应用，我们研究了周期性边界条件下的二维完全共振梁系统。利用 KAM 定理和部分伯克霍夫正态法，我们得到了方程系统的惠特尼光滑小振幅准周期解系列。
KAM tori for two dimensional completely resonant derivative beam system
In this paper, we introduce an abstract KAM (Kolmogorov–Arnold–Moser) theorem. As an application, we study the two-dimensional completely resonant beam system under periodic boundary conditions. Using the KAM theorem together with partial Birkhoff normal form method, we obtain a family of Whitney smooth small–amplitude quasi–periodic solutions for the equation system.
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