Quasi-periodic response solutions in forced reversible systems with Liouvillean frequencies

This paper is concerned with the existence of quasi-periodic response solutions for a class of reversible forced harmonic oscillators with two basic frequencies ω=(1,α), α is an irrational number. Since we do not impose usual Diophantine or Brjuno conditions on ω, it can also be Liouvillean. The proof is based on a modified KAM (Kolmogorov-Arnold-Moser) theorem for reversible systems.