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

H.W. Broer and C. Sim\'o

Abstract 

A linear system in two dimensions is studied. The coefficients are 
2pi-periodic on three angles, theta_j,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 a three torus time a 2D plane, however,
is only of class L^p, for any p<2.