Rigidity for circle diffeomorphisms with breaks satisfying a Zygmund smoothness condition

2021/07/23 by Akhadkulov, H. A., Dzhalilov, A. A., Khanin, K. M.
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.12905

Abstract

Let f and f be two circle diffeomorphisms with a break point, with the same irrational rotation number of bounded type, the same size of the break c and satisfying a certain Zygmund type smoothness condition depending on a parameter γ>2. We prove that under a certain condition imposed on the break size c, the diffeomorphisms f and f are C^1+ω_γ-smoothly conjugate to each other, where ω_γ(δ)=|log δ|^-(γ/2-1).

Related

• Circle homeomorphisms with breaks with no C^2-ν conjugacy
• Smooth linearization of commuting circle diffeomorphisms
• Rigidity for piece-wise smooth circle maps and certain GIETs
• Nonrigidity of piecewise-smooth circle maps
• Renormalization of circle diffeomorphisms with a break-type singularity