Rigidity of critical circle mappings, I

1997/11/15 by Edson de Faria, de Faria, Edson, Welington de Melo +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.math/9711214

openalex publication_date 1997/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that two C^r critical circle maps with the same rotation number of bounded type are C^1+α conjugate for some α>0 provided their successive renormalizations converge together at an exponential rate in the C⁰ sense. The number α depends only on the rate of convergence. We also give examples of C^∞ critical circle maps with the same rotation number that are not C^1+β conjugate for any β>0.

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