# A new approach to the family of singularities $Rex iy^m$ - Mathematics > Functional Analysis

A new approach to the family of singularities $Rex iy^m$ - Mathematics > Functional Analysis - Download this document for free, or read online. Document in PDF available to download.

Abstract: Assume that $m\ge 2$ and let $l$ be a nonnegative integer with $l\ge m-4$. Wegive an alternative proof of the fact that any smooth function defined locallyaround $0,0\in \mathbb{R}^2$ with the Taylor power series at $0,0$beginning with $$Rex+iy^m+0+ .+0$$ $l$ zeros is diffeomorphicallyequivalent to $Rex+iy^m$ at $0,0$. For $m\ge 5$ and $C e 0$ we show thatthe function $$Rex+iy^m+Cx^2+y^2^{m-2}$$ is not diffeomorphicallyequivalent to $Rex+iy^m$ at $0,0$.

Author: Evgeny Volkov

Source: https://arxiv.org/