On lower dimensional invariant tori in reversible systems (Q5955607)

The author studies the existence of \(n\)-dimensional tori of the system NEWLINE\[NEWLINE\begin{aligned} & \dot x=\Lambda_1(y,u,v)+F_1(x,y,u,v),\\ & \dot y=\Lambda_2(y,u,v)+F_2(x,y,u,v),\\ & \dot u = L_1(y,u,v) +F_3 (x,y,u,v),\\ & \dot v = L_2(y,u,v) +F_4 (x,y,u,v),\end{aligned}\tag{1}NEWLINE\]NEWLINE where \((x,y,u,v)\in\mathbb{T}^n\times \mathbb{R}^n\times\mathbb{R}^n\times\mathbb{R}^p\times \mathbb{R}^q\), and \(F_j\), \(1\leq j\leq 4\), are given real-analytic in a complex neighborhood of a real domain \(\{(x,y,u,v)\mid x\in\mathbb{T}^n\), \(y\in D\), \(u=0,v=0\}\) with an open set \(D\in\mathbb{R}^n\). The author obtains a result on the persistence of lower-dimensional tori for a general class of reversible systems of the form (1).