The Denjoy type of argument for quasiperiodically forced circle diffeomorphisms

Abstract

We carry the argument used in the proof of Denjoy's theorem over to the quasiperiodically forced case. Thus we derive that, if a system of quasiperiodically forced circle diffeomorphisms with bounded variation of the derivative has no invariant graphs with a certain kind of topological regularity, then the system is topologically transitive. © 2006 Cambridge University Press.