Weighted Homogeneous Polynomials with Isomorphic Milnor Algebras

Abstract

We recall first some basic facts on weighted homogeneous functions and filtrations in the ring $A$ of formal power series. We introduce next their analogues for weighted homogeneous diffeomorphisms and vector fields. We show that the Milnor algebra is a complete invariant for the classification of weighted homogeneous polynomials with respect to right-equivalence, i.e. change of coordinates in the source and target by diffeomorphism.