保留马丁内特形式的三维矢量场的奇异性

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2024-07-27 DOI:10.1134/S0040577924070018

S. Anastassiou

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引用次数: 0

摘要

Abstract 我们研究了在\(\mathbb{R}^3\)上保持Martinet \(1\)-形式 \(\alpha=(1+x)dy\pm z\,dz\) 的向量场的局部结构。我们对它们的奇点进行了分类，直到保留了形式（\α）的差分变形，以及它们的横向展开。因此，我们能够提供一份相当完整的清单，列出这些向量场所经历的分岔。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Singularities of 3D vector fields preserving the Martinet form

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Singularities of 3D vector fields preserving the Martinet form

We study the local structure of vector fields on \(\mathbb{R}^3\) that preserve the Martinet \(1\)-form \(\alpha=(1+x)dy\pm z\,dz\). We classify their singularities up to diffeomorphisms that preserve the form \(\alpha\), as well as their transverse unfoldings. We are thus able to provide a fairly complete list of the bifurcations such vector fields undergo.

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来源期刊

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.