A Denjoy Theorem for commuting circle diffeomorphisms with mixed Holder derivatives

2007/04/08 by Victor Kleptsyn, Kleptsyn, Victor, Andrés Navas +2
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 #math.DS

paper · pdf · doi:10.48550/arxiv.0704.1006

14 pages, 4 figures

arxiv created 2007/04/08 · openalex publication_date 2007/04/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that if d is an integer number bigger than 1 and f₁,...,f_d are commuting circle diffeomorphisms respectively of class C^(1+τ_k), where τ₁ + ... + τ_k > 1, then these maps are simultaneously conjugate to rotations provided that their rotation numbers are independent over the rationals.

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