不带$\bold符号{C^{2-\nu}}$共轭的带断点的圆同胚

IF 0.7 1区 数学 Q2 MATHEMATICS
Nataliya Goncharuk, Konstantin Khanin, Yury Kudryashov
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引用次数: 0

摘要

带断裂的圆同胚的刚性理论是近20年来研究的热点。证明了[15,21,17,19]在旋转数上Diophantine型的温和条件下,任意两个具有断点的$C^{2+\alpha}$光滑圆同纯互为$C^1$平滑共轭,只要它们具有相同的旋转数和相同的断点大小。在本文中,我们证明了即使映射在断点外是解析的,共轭也可能不为$C^{2-\nu}$。这一结果表明,奇异映射的刚性理论与圆微分同态的线性化情况有很大的不同,圆微分同态的共轭是任意光滑的,甚至是解析的,对于足够光滑的微分同态。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Circle homeomorphisms with breaks with no $\boldsymbol{C^{2-\nu}}$ conjugacy
The rigidity theory for circle homeomorphisms with breaks has been studied intensively in the last 20 years. It was proved [15, 21, 17, 19] that under mild conditions of the Diophantine type on the rotation number any two $C^{2+\alpha}$ smooth circle homeomorphisms with a break point are $C^1$ smoothly conjugate to each other, provided that they have the same rotation number and the same size of the break. In this paper we prove that the conjugacy may not be $C^{2-\nu}$ even if the maps are analytic outside of the break points. This result shows that the rigidity theory for maps with singularities is very different from the linearizable case of circle diffeomorphisms where conjugacy is arbitrarily smooth, or even analytic, for sufficiently smooth diffeomorphisms.
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
11
审稿时长
>12 weeks
期刊介绍: The Journal of Modern Dynamics (JMD) is dedicated to publishing research articles in active and promising areas in the theory of dynamical systems with particular emphasis on the mutual interaction between dynamics and other major areas of mathematical research, including: Number theory Symplectic geometry Differential geometry Rigidity Quantum chaos Teichmüller theory Geometric group theory Harmonic analysis on manifolds. The journal is published by the American Institute of Mathematical Sciences (AIMS) with the support of the Anatole Katok Center for Dynamical Systems and Geometry at the Pennsylvania State University.
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