Birkhoff Program for Geodesic Flows of Surfaces and Applications: Homoclinics

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-09 DOI:10.1007/s10884-024-10349-8

Gonzalo Contreras, Fernando Oliveira

引用次数: 0

Abstract

We show that a Kupka–Smale riemannian metric on a closed surface contains a finite primary set of closed geodesics, i.e. they intersect any other geodesic and divide the surface into simply connected regions. From them we obtain a finite set of disjoint surfaces of section of genera 0 or 1, which intersect any orbit of the geodesic flow. As an application we obtain that the geodesic flow of a Kupka–Smale riemannian metric on a closed surface has homoclinic orbits for all branches of all of its hyperbolic closed geodesics.

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表面大地流的伯克霍夫程序及其应用：同次元

我们证明，封闭曲面上的库普卡-斯马尔（Kupka-Smale）江曼度量包含有限的封闭测地线主集，即它们与任何其他测地线相交，并将曲面划分为简单相连的区域。由此我们可以得到一个有限的 0 或 1 类截面的不相交曲面集合，这些曲面与任意大地流轨道相交。作为应用，我们可以得到，封闭曲面上的库普卡-斯马尔（Kupka-Smale）里曼矩阵的测地流在其所有双曲封闭测地线的所有分支上都有同极坐标轨道。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.