Stoker's problem for quasi-periodically forced reversible systems with multi-dimensional Liouvillean frequency

In this paper, we develop KAM (Kolmogorov-Arnold-Moser) theorem for a class of quasi-periodically forced reversible systems with multi-dimensional Liouvillean frequency. The proof does not need the CD-bridge given by Avila, Fayad and Krikorian, which has been used in many literatures. Our results are directly
applicable to Stoker's problem of quasi-periodically forced reversible harmonic oscillators with multi-dimensional Liouvillean frequency.