Weighted homogeneous polynomials with isomorphic milnor algebras
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JPRM-Vol. 1 (2012), Issue 1, pp. 106 – 114 Open Access Full-Text PDF
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.