Peng HUANG
In this paper, we consider the persistence of invariant tori in the following system \begin{equation*} \begin{array}{ll} \left\{\begin{array}{ll} \dot{x}=\omega+y+f(x,y),\\[0.1cm] \dot{y}=g(x,y), \end{array}\right. \end{array} \end{equation*} where $x\in \mathbb{T}^\Lambda$, $y\in\mathbb{R}^\Lambda$, $\Lambda$ is a countable subset of $\mathbb{Z}$, ${\omega}=(\ldots,{\omega}_\lambda,\ldots)_{\lambda\in \Lambda}\in\mathbb{R}^\Lambda$ is the frequency vector, ${\omega}=(\ldots,{\omega}_\lambda,\ldots)_{\lambda\in \Lambda}$ is a bilateral infinite sequence of rationally independent frequency, in other words, any finite segments of ${\omega}=(\ldots,{\omega}_\lambda,\ldots)_{\lambda\in \Lambda}$ are rationally independent, and the perturbations $f, g$ are real analytic functions. We also assume that the above system is reversible with respect to the involution $\mathcal{M }: (x,y) \mapsto (-x,y)$. By the KAM method, we prove the persistence of invariant tori for the above reversible system.
