Commuting circle diffeomorphisms with their derivatives having mixed moduli of continuity

2019/04/08 by Hui Xu, Xu, Hui, Enhui Shi +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1904.03984

openalex publication_date 2019/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let d≥ 2 be an integer and let ω₁,⋯ ,ω_d be moduli of continuity in a specified class which contains the moduli of Hölder continuity. Let f_k, k∈\1,⋯,d\, be C^1+ω_k orientation preserving diffeomorphisms of the circle and f₁,⋯, f_d commute with each other. We prove that if the rotation numbers of f_k's are independent over the rationals and ω₁(t)⋯ω_d(t)=tω(t) with lim_{t→ 0⁺}ω(t)=0, then f₁,⋯,f_d are simultaneously (topologically) conjugate to rigid rotations.

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