Work

Reducing smooth functions to normal forms near critical points

Year: 2022

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2206.00628

Author: Orevkova, A. S.

Institutions: Lomonosov Moscow State University, Moscow Center of Fundamental and Applied Mathematics

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4281908155

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