Constructing Birkhoff sections for pseudo-Anosov flows with controlled complexity

IF 0.8 3区数学 Q2 MATHEMATICS

Ergodic Theory and Dynamical Systems Pub Date : 2023-11-14 DOI:10.1017/etds.2023.105

CHI CHEUK TSANG

引用次数: 4

Abstract

Abstract We introduce a new method of constructing Birkhoff sections for pseudo-Anosov flows, which uses the connection between pseudo-Anosov flows and veering triangulations. This method allows for explicit constructions, as well as control over the Birkhoff section in terms of its Euler characteristic and the complexity of the boundary orbits. In particular, we show that any transitive pseudo-Anosov flow has a Birkhoff section with two boundary components.

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构造具有控制复杂性的伪anosov流的Birkhoff区段

摘要利用伪anosov流与转向三角剖分之间的联系，提出了一种构造伪anosov流Birkhoff截面的新方法。这种方法允许显式构造，以及根据其欧拉特性和边界轨道的复杂性对Birkhoff截面进行控制。特别地，我们证明了任何传递伪anosov流都有一个具有两个边界分量的Birkhoff截面。

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.