Reducible linear quasi-periodic systems with positive Lyapunov exponent and varying rotation number

A linear system in two dimensions is studied. The coefficients are 2 pi -periodic in three angles, 0(j), = 1, 2, 3, and these angles are linear with respect to time, with incommensurable frequencies. The system has positive Lyapunov coefficients and the rotation number changes in a continuous way when some parameter moves. A lift to T-3 x R-2, however, is only of class L-p, for any p <2. (C) 2000 Academic Press.