Abstract

Since Keller studied, in 1996, the existence of Strange Nonchaotic Attractors in a particular kind of two-dimensional quasiperiodically forced skew-products defined on (M^+:=mathbb{S}1times[0,infty)), several extensions of his results have been published. All these extensions have in common that the system are defined on (M^+), and the component on the basis is always an irrational rotation. We extend Keller and Haro results to similar systems defined on (mathbb{S}1timesmathbb{R}), in this case we can have two attractors given by the graph of a map defined on (mathbb{S}1) or only one given by the graph of a two-valued correspondence. If we exchange the irrational rotation by a Denjoy counterexample, the results are quite similar with the difference that the map, or correspondence, whose graph gives the attractor is defined on (Psubsetmathbb{S}1), where (P) is the support of the unique invariant measure of the Denjoy counterexample.