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 $C^{\infty}$ 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 $C^\infty$-topology. 
Raphael Krikorian, Jing Wang, Jiangong You, Qi Zhou
math.DS