A normal form theorem for Brjuno skew systems through renormalization

We develop a dynamical renormalization method for the problem of local reducibility of analytic linear quasi-periodic skew-product flows on T2×SL(2,R). This approach is based on the continued fraction expansion of the linear base flow and deals with “small-divisors” by turning them into “large-divisors.” We use this method to give a new proof of a normal form theorem for a Brjuno base flow.