Liviana Palmisano: Quasi-symmetric conjugacy for circle maps with a flat interval

We study quasi-symmetric conjugations of C² weakly order-preserving circle maps with a flat interval. Under the assumption that the maps have the same rotation number of bounded type and that bounded geometry holds we construct a quasi-symmetric conjugation between their non-wandering sets. Further, this conjugation is extended to a quasi-symmetric circle homeomorphism.

Our proof techniques hinge on real-dynamic methods allowing us to construct the conjugation under general and natural assumptions.

A more general setting of circle functions with unbounded rotation numbers is also studied. We discuss problems arising in this case and some possible developments.