Response solutions for quasi-periodically forced harmonic oscillators in Gevrey class
Response solutions for quasi-periodically forced harmonic oscillators in Gevrey class
复制标题
DOI：
10.1016/j.jde.2023.01.034
复制
发表时间：
2023-05
影响因子：
2.4
通讯作者：
Jing Wang;Huijuan Wei;Xindong Xu
中科院分区：
文献类型：
--
作者：
Jing Wang;Huijuan Wei;Xindong Xu
证明了对于拟周期强迫谐振子，如果强迫频率ω∈r2 \ q2是非谐振的，并且强迫是部分Gevrey光滑的，则存在响应解。这将结果推广到[22]，其中强迫项是实解析项。对低维不变环面进行了改进的KAM理论证明。
We prove that for quasi-periodically forced harmonic oscillator, if the forcing frequency ω∈ R 2﹨ Q 2 is non-resonant and the forcing is partial Gevrey smooth, then there exist response solutions. This generalized the result by [22] where the forcing term is real analytic. The proof is based on modified KAM theory for lower dimensional invariant tori.