Old and New Results on Snas on the Real Line

Classical and new results concerning the topological structure of skew-products semiflows, coming from non-autonomous maps and differential equations, are combined in order to establish rigorous conditions giving rise to the occurrence of strange nonchaotic attractors. A special attention is paid to the relation of these sets with the almost automorphic extensions of the base flow. The scope of the results is clarified by applying them to the Harper map, although they are valid in a much wider context.