Denjoy C1 diffeomorphisms of the circle and McDuff’s question

In this expository article, after the basic theory of orientation preserving C1C1 diffeomorphisms of the circle, we present D. McDuff’s theorem on the lengths of the complementary intervals of the unique Cantor minimal set of a Denjoy C1C1 diffeomorphism of the circle. This leads to a question posed by Dusa McDuff which is related to the solvability of a cohomological equation on the Cantor set.