Dynamical Description of Bidimensional Linear Systems with a Measurable 2-Sheet

The dynamical behaviour of the projective flow induced by a family of bidimensional linear systems with a measurable 2-sheet is studied. When the Lyapunov exponent vanishes, it is shown that the trajectories move from one sheet to the other either when t tends to q` or y`. This extends and completes some known results on oscillatory dynamics to a more general ergodic situation.