V. S. Kozyakin
Rotation numbers of discontinuous orientation-preserving circle maps revisited
The theory of circle homeomorphisms has a great number of deep results. However, sometimes continuity or single-valuedness of a circle map may be restrictive in theoretical constructions or applications. In this paper it is shown that some principal properties of circle homeomorphisms are inherited by the class of orientation-preserving circle maps. The latter class is rather broad and contains not only circle homeomorphisms but also a variety of non continuous maps arising in applications. Of course, even in cases when a property remains to be valid for orientation-preserving circle maps, absence of continuity sometimes results in noticeable changes of related proofs.