A new approach to the family of singularities $Re(x+iy)^m$
| dc.creator | Volkov, Evgeny | |
| dc.date | 2008-09-17 | |
| dc.date.accessioned | 2026-07-07T10:03:29Z | |
| dc.date.available | 2026-07-07T10:03:29Z | |
| dc.description | Assume that $m\ge 2$ and let $l$ be a nonnegative integer with $l\ge m-4$. We give an alternative proof of the fact that any smooth function defined locally around $(0,0)\in \mathbb{R}^2$ with the Taylor power series at $(0,0)$ beginning with $$Re(x+iy)^m+0+...+0$$ ($l$ zeros) is diffeomorphically equivalent to $Re(x+iy)^m$ at $(0,0)$. For $m\ge 5$ and $C\ne 0$ we show that the function $$Re(x+iy)^m+C(x^2+y^2)^{m-2}$$ is not diffeomorphically equivalent to $Re(x+iy)^m$ at $(0,0)$. | |
| dc.description | 27 pages | |
| dc.identifier | https://arxiv.org/abs/0809.2868 | |
| dc.identifier | http://arxiv.org/abs/0809.2868 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169305 | |
| dc.subject | Functional Analysis | |
| dc.subject | 58K05 | |
| dc.title | A new approach to the family of singularities $Re(x+iy)^m$ | |
| dc.type | text |