ALMOST EVERYWHERE REDUCIBILITY OF ANALYTIC QUASI-PERIODIC SYSTEMS IN THE SO(3) CASE

We prove, answering a question by L. H. Eliasson in [4], that given [a: b] subset of R, omega is an element of R(d) some diophantine frequency vector and A not equal 0 in so (3, R) (the set of skew symetric 3 x 3 matrices), the set of parameters lambda is an element of [a, b], for which the so (3, R)-valued system lambda A + F (omega t) is not reducible,is of Lebesgue measure zero, provided the analytic omega-quasipei-iodic perturbation F is small enough.