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arXiv · 2206.00628

Reducing smooth functions to normal forms near critical points

A. S. Orevkova
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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.

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A. S. Orevkova. 2022-06-01. Reducing smooth functions to normal forms near critical points. https://arxiv.org/abs/2206.00628

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