On the Regularity of Invariant Foliations

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI:10.1134/S1560354724010027

Dmitry Turaev

引用次数: 0

Abstract

We show that the stable invariant foliation of codimension 1 near a zero-dimensional hyperbolic set of a \(C^{\beta}\) map with \(\beta>1\) is \(C^{1+\varepsilon}\) with some \(\varepsilon>0\). The result is applied to the restriction of higher regularity maps to normally hyperbolic manifolds. An application to the theory of the Newhouse phenomenon is discussed.

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论不变叶形的规律性

我们证明了在零维双曲集合附近，具有 \(C^{beta>1\) 的 \(C^{1+\varepsilon}\) 映射的标度为 1 的稳定不变叶面是具有某种 \(\varepsilon>0\) 的 \(C^{1+\varepsilon}\)。这一结果被应用于高正则映射对正常双曲流形的限制。讨论了纽豪斯现象理论的应用。

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

Regular and Chaotic Dynamics 物理-力学

CiteScore

2.50

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.