Global Density of Reducible Quasi-Periodic Cocycles on T 1 × SU(2)

Abstract

We prove that given a in a set of total (Haar) measure in T 1 = R/Z, the set of A ∈ C ∞ (T 1 , SU(2)) for which the skew-product system (α, A): T 1 × SU(2) → T 1 × SU(2), (α, A)(θ,y) = (θ + α, A(θ)y) is reducible - that is, A(.) = B(.+ α)A 0 B(.) - 1 , for some A 0 ∈ SU(2), B ∈ C ∞ (T 1 , SU(2)),- is dense for the C°°-topology.