Renormalization of circle maps and smoothness of Arnold tongues

2023/07/27 by Nataliya Goncharuk, Goncharuk, Nataliya, Michael Yampolsky +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2307.15195

openalex publication_date 2023/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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