Reducible Linear Quasi-periodic Systems with Positive Lyapunov Exponent and Varying Rotation Number

A linear system in two dimensions is studied. The coefficients are 2π-periodic in three angles, θj, 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 3× 2, however, is only of class Lp, for any p<2.