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arXiv · 2107.12905

Rigidity for circle diffeomorphisms with breaks satisfying a Zygmund smoothness condition

H. A. Akhadkulov·A. A. Dzhalilov·K. M. Khanin
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Abstract

Let $f$ and $\tilde{f}$ 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 $\gamma>2.$ We prove that under a certain condition imposed on the break size $c$, the diffeomorphisms $f$ and $\tilde{f}$ are $C^{1+\omega_{\gamma}}$-smoothly conjugate to each other, where $\omega_{\gamma}(\delta)=|\log \delta|^{-(\gamma/2-1)}.$

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H. A. Akhadkulov, A. A. Dzhalilov, K. M. Khanin. 2021-07-23. Rigidity for circle diffeomorphisms with breaks satisfying a Zygmund smoothness condition. https://arxiv.org/abs/2107.12905

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