Response solutions for quasi-periodically forced harmonic oscillators
Response solutions for quasi-periodically forced harmonic oscillators
复制标题
准周期受迫谐振子的响应解
DOI：
10.1090/tran/6800
复制
发表时间：
2017
影响因子：
1.3
通讯作者：
Zhou Qi
中科院分区：
文献类型：
--
作者：
Wang Jing;You Jiangong;Zhou Qi
本文证明了当强迫较小时，具有两个频率的非线性拟周期受迫谐振子至少有一个响应解。该结果不需要对频率作任何算术条件，也不依赖于非线性强迫的微小性，加强了已有文献中假设频率为丢番图的结果。证明是基于一个修改后的KAM理论的低维环面。引用
We prove that the non-linear quasi-periodically forced harmonic oscillator with two frequencieshas at least one response solution if the forcing is small. No arithmetic condition on the frequency is assumed and the smallness of the non-linear forcing does not depend on. The result strengthens the existing results in the literature where the frequency is assumed to be Diophantine. The proof is based on a modified KAM theory for the lower dimensional tori. References