表面大地流的伯克霍夫程序及其应用：同次元

IF 1.4 4区数学 Q1 MATHEMATICS

Journal of Dynamics and Differential Equations Pub Date : 2024-03-09 DOI:10.1007/s10884-024-10349-8

Gonzalo Contreras, Fernando Oliveira

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引用次数: 0

摘要

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。

Birkhoff Program for Geodesic Flows of Surfaces and Applications: Homoclinics

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Birkhoff Program for Geodesic Flows of Surfaces and Applications: Homoclinics

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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来源期刊

Journal of Dynamics and Differential Equations 数学-数学

CiteScore

3.30

自引率

7.70%

发文量

116

审稿时长

>12 weeks

期刊介绍： Journal of Dynamics and Differential Equations serves as an international forum for the publication of high-quality, peer-reviewed original papers in the field of mathematics, biology, engineering, physics, and other areas of science. The dynamical issues treated in the journal cover all the classical topics, including attractors, bifurcation theory, connection theory, dichotomies, stability theory and transversality, as well as topics in new and emerging areas of the field.