Renormalization of circle maps and smoothness of Arnold tongues
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.
Authors
- Nataliya Goncharuk (ORCID: https://orcid.org/0000-0002-4270-0510)
- Michael Yampolsky
Institutions
- University of Toronto (CA)
- Mitchell Institute (US)
- Texas A&M University (US)
Publication Details
- Journal
- Ergodic Theory and Dynamical Systems
- Published
- 2025-02-24
- DOI
- https://doi.org/10.1017/etds.2025.2
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- article
- Field-Weighted Citation Impact
- 0.00