Finiteness theorem for multi‐‐bi‐Lipschitz equivalence of map germs

Abstract

Let Pkfalse(n,pfalse) be the set of all real polynomial map germs f=false(f1,⋯,fpfalse):false(Rn,0false)→false(Rp,0false) with degree of f1,⋯,fp less than or equal to k∈N. The main result of this paper shows that the set of equivalence classes of Pkfalse(n,pfalse), with respect to multi‐scriptK‐bi‐Lipschitz equivalence, is finite.