$C^r$-right equivalence of analytic functions

Piotr Migus

Let $f,g:({\mathbb{R}}^n,0)\to (\mathbb{R},0)$ be analytic functions. We will show that if $\nabla f(0)=0$ and $g-f\in (f{)}^{r+2}$ then $f$ and $g$ are $C^r$-right equivalent…