Linearization of quasiperiodically forced circle flow beyond Brjuno condition

We prove that an analytic quasiperiodically forced circle flow with a not super-Liouvillean base frequency and which is close enough to some constant rotation is $C^{\mathrm{\infty }}$ rotations reducible, provided its fibered rotation number is Diophantine with respect to the base frequency. As a corollary, we obtain that among such systems, the linearizable ones and those displaying mode-locking are locally dense for the $C^{\mathrm{\infty }}$-topology.