A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class

IF 0.8 3区数学 Q2 MATHEMATICS

Ergodic Theory and Dynamical Systems Pub Date : 2023-11-03 DOI:10.1017/etds.2023.76

Bonatti, Christian, Shinohara, Katsutoshi

引用次数: 1

Abstract

Abstract We give a $C^1$ -perturbation technique for ejecting an a priori given finite set of periodic points preserving a given finite set of homo/heteroclinic intersections from a chain recurrence class of a periodic point. The technique is first stated under a simpler setting called a Markov iterated function system, a two-dimensional iterated function system in which the compositions are chosen in a Markovian way. Then we apply the result to the setting of three-dimensional partially hyperbolic diffeomorphisms.

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从部分双曲链递推类中弹出马蹄形的机制

摘要给出了一种$C^1$摄动技术，用于从周期点的链式递推类中导出一个先验的给定有限周期点集，并保留了一个给定有限的同/异斜交点集。该技术首先在一种称为马尔可夫迭代函数系统的简单设置下陈述，这是一种二维迭代函数系统，其中以马尔可夫方式选择组合。然后将结果应用于三维部分双曲微分同态的设置。

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

Ergodic Theory and Dynamical Systems 数学-数学

CiteScore

1.70

自引率

11.10%

发文量

113

审稿时长

6-12 weeks

期刊介绍： Ergodic Theory and Dynamical Systems focuses on a rich variety of research areas which, although diverse, employ as common themes global dynamical methods. The journal provides a focus for this important and flourishing area of mathematics and brings together many major contributions in the field. The journal acts as a forum for central problems of dynamical systems and of interactions of dynamical systems with areas such as differential geometry, number theory, operator algebras, celestial and statistical mechanics, and biology.