在临界点附近将光滑函数化简为正规形式

Q4 Mathematics

Chebyshevskii Sbornik Pub Date : 2022-06-01 DOI:10.22405/2226-8383-2022-23-5-101-116

A. S. Orevkova

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引用次数: 0

摘要

本文研究了2-流形上的光滑函数在临界点附近的“一致”化约为正则形式，方法是在这些点的某些邻域上的一些坐标变化。对于奇异类型$E_6,E_8$和$A_n$，我们显式地构造这样的坐标变化，并从下面(根据函数的$C^r$-范数)估计所需邻域的半径。

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Reducing smooth functions to normal forms near critical points

The paper is devoted to"uniform"reduction of smooth functions on 2-manifolds to canonical form near critical points by some coordinate changes in some neighbourhoods of these points. For singularity types $E_6,E_8$ and $A_n$, we explicitly construct such coordinate changes and estimate from below (in terms of $C^r$-norm of the function) the radius of a required neighbourhood.

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来源期刊

Chebyshevskii Sbornik Mathematics-Mathematics (all)

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： The aim of the journal is to publish and disseminate research results of leading scientists in many areas of modern mathematics, some areas of physics and computer science.