Strange non-chaotic attractors in quasiperiodically forced circle maps

Understand

The occurrence of strange non-chaotic attractors (SNA) in quasiperiodically forced systems has attracted considerable interest over the last two decades, in particular since it provides a rich class of examples for the possibility of complicated dynamics in the absence of chaos.

• Their existence was discovered in the early 1980's, independently by Herman for quasiperiodic SL(2,R)-cocycles and by Grebogi et al for so-called 'pinched skew products'.
• However, except for these two particular classes there are still hardly any rigorous results on the topic, despite a large number of numerical studies which all confirmed the widespread existence of SNA in quasiperiodically forced systems.
• Here, we prove the existence of SNA in quasiperiodically forced circle maps under rather general conditions, which can be stated in terms of C 1 -estimates.