A note on strange nonchaotic attractors

For a class of quasiperiodically forced time-discrete dynamical systems of two variables (theta,x) epsilon T-1 x R(+) with nonpositive Lyapunov exponents we prove the existence of an attractor <(Gamma)over bar> with the following properties: 1. <(Gamma)over bar> is the closure of the graph of a function x = phi(theta). It attracts Lebesgue-a.e. starting point in T-1 x R(+). The set {theta:phi(theta} not equal 0) is meager but has full 1-dimensional Lebesgue measure. 2. The omega-limit of Lebesgue-a.e. point in T-1 x R(+) is <(Gamma)over bar>, but for a residual set of points in T-1 x R(+) the omega limit is the circle {(theta,x) :x = 0} contained in <(Gamma)over bar>. 3. <(Gamma)over bar> is the topological support of a BRS measure. The corresponding measure theoretical dynamical system is isomorphic to the forcing rotation.