Finitness theorem for Multi-K-Bi-Lipschtiz equivalence of map-germs

Abstract

Let $P^k(n,p)$ be the set of all real polynomial map germs $f=(f_1,...,f_p):({\mathbb{R}}^n,0)\to ({\mathbb{R}}^p,0)$ with degree of $f_1,...,f_p$ less than or equal to $k\in \mathbb{N}$. The main result of this paper shows that the set of equivalence classes of $P^k(n,p)$, with respect to multi-$\mathcal{K}$-bi-Lipschitz equivalence, is finite.

10 pages