ON RESIDUES AND CONJUGACIES FOR GERMS OF 1-D PARABOLIC DIFFEOMORPHISMS IN FINITE REGULARITY

IF 1.1 2区数学 Q1 MATHEMATICS Journal of the Institute of Mathematics of Jussieu Pub Date : 2023-12-01 DOI:10.1017/s1474748023000403

Hélène Eynard-Bontemps, Andrés Navas

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引用次数: 1

Abstract

We study conjugacy classes of germs of nonflat diffeomorphisms of the real line fixing the origin. Based on the work of Takens and Yoccoz, we establish results that are sharp in terms of differentiability classes and order of tangency to the identity. The core of all of this lies in the invariance of residues under low-regular conjugacies. This may be seen as an extension of the fact (also proved in this article) that the value of the Schwarzian derivative at the origin for germs of

$C^3$

parabolic diffeomorphisms is invariant under

$C^2$

parabolic conjugacy, though it may vary arbitrarily under parabolic

$C^1$

conjugacy.

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有限规则下一维抛物型微分同态胚芽的残数和共轭性

研究了固定原点的实直线的非平微分同态胚芽的共轭类。基于Takens和Yoccoz的工作，我们建立了关于恒等式的可微性类和切线阶的尖锐结果。这一切的核心在于低正则共轭下残数的不变性。这可以看作是一个事实的扩展(也在本文中证明了)，即C^3$抛物型微分同态的胚在原点处的Schwarzian导数值在C^2$抛物型共轭下是不变的，尽管它在C^1$抛物型共轭下可以任意变化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of the Institute of Mathematics of Jussieu 数学-数学

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of the Institute of Mathematics of Jussieu publishes original research papers in any branch of pure mathematics; papers in logic and applied mathematics will also be considered, particularly when they have direct connections with pure mathematics. Its policy is to feature a wide variety of research areas and it welcomes the submission of papers from all parts of the world. Selection for publication is on the basis of reports from specialist referees commissioned by the Editors.

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