Almost everywhere reducibility of quasi-periodic fibered flows with valuesin compact groups.

Let us be given a compact "semi-simple" Lie group G with Lie algebra g, a r egular element A is an element of g, a bounded interval Lambda subset of R and a diophantine vector omega is an element of R-d: then if F is an elemen t of C-omega(R-d/Z(d), g) is small enough, omega meaning here "real analyti c", for Lebesgue-a.e. lambda is an element of Lambda, thr quasi-periodic sy stem lambda A + F(omega(1)/2 pi t,...,omega(d)/2 pi t), with frequency vect or w, is Floquet-reducible module some finite covering depending only on th e group G. This theorem is a generalization of the one proved in [5]. (C) E lsevier, Paris.