Linearization of Quasi-Periodically Forced Circle Flows Beyond Multi-Dimensional Brjuno Frequency.

This paper focuses on the vector fields on the quasi-periodically forced circle flow φ ˙ = ρ + f (φ , θ) , θ ˙ = α where the forcing term f is real analytic in its arguments and small enough, the frequency vector α ∈ R d (d ≥ 2) is beyond Brjuno frequency. We prove that the flow above is reducible analytically provided fibered rotation number ρ f : = ρ (ρ + f (φ , θ)) is Diophantine with respect to the base frequency α. The proof is based on a modified KAM (Kolmogorov–Arnold–Moser) theorem for finite-dimensional systems with multi-dimensional frequency weaker than Brjuno frequency. [ABSTRACT FROM AUTHOR]