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math.DS2023
Renormalization and scaling of bubbles
Nataliya Goncharuk, Igors Gorbovickis
The paper explores scaling properties of bubbles -- a complex analogue of Arnold tongues, associated to a one-dimensional family of analytic circle diffeomorphisms. Bubbles are smo…
math.DS2023
Renormalization of circle maps and smoothness of Arnold tongues
Nataliya Goncharuk, Michael Yampolsky
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 diffeomorphis…