Renormalization of circle maps and smoothness of Arnold tongues

Nataliya Goncharuk, Michael Yampolsky

Published 2023-07-27Version 1

We study the global behavior of the renormalization operator on a specially constructed Banach manifold that has cubic critical circle maps on its boundary and circle diffeomorphisms in its interior. As an application, we prove results on smoothness of irrational Arnold tongues.