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 -pe riodic in three angles, 0(j), = 1, 2, 3, and these angles are linear with r espect to time, with incommensurable frequencies. The system has positive L yapunov coefficients and the rotation number changes in a continuous way wh en 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.