Journal of Dynamics and Differential Equations ( IF 1.3 ) Pub Date : 2021-06-26 , DOI: 10.1007/s10884-021-10032-2 Hongyu Cheng
This paper focuses on the vector fields on the quasi-periodically forced circle flow
$$\begin{aligned} \left\{ \begin{array}{l} {\dot{\varphi }}=\rho +f(\varphi ,\theta ),\\ \\ {\dot{\theta }}=\alpha \end{array} \right. \end{aligned}$$where the forcing term f is real analytic in its arguments and small enough, the frequency vector \( \alpha \in {\mathbb {R}}^d (d\ge 2)\) is beyond Brjuno frequency. We prove that the flow above is reducible analytically provided fibered rotation number \(\rho _{f}:=\rho (\rho +f(\varphi ,\theta ))\) is Diophantine with respect to the base frequency \(\alpha .\) The proof is based on a modified KAM (Kolmogorov–Arnold–Moser) theorem for finite-dimensional systems with multi-dimensional frequency weaker than Brjuno frequency.
中文翻译：
超多维 Brjuno 频率的准周期性受力圆流的线性化
本文重点研究了准周期性受力圆周流上的矢量场
$$\begin{aligned} \left\{ \begin{array}{l} {\dot{\varphi }}=\rho +f(\varphi ,\theta ),\\ \\ {\dot{\theta }}=\alpha \end{array} \right。\end{对齐}$$其中强制项f在其参数中是实解析的并且足够小，频率向量\( \alpha \in {\mathbb {R}}^d (d\ge 2)\)超出了 Brjuno 频率。我们证明上面的流程是可还原的分析提供的纤维旋转数\(\rho _{f}:=\rho (\rho +f(\varphi ,\theta ))\)相对于基频\( \alpha .\)该证明基于多维频率弱于 Brjuno 频率的有限维系统的修正 KAM（Kolmogorov-Arnold-Moser）定理。
京公网安备 11010802027423号