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Existence of Moduli for Bi-Lipschitz Equivalence of Analytic Functions
Authors:Jean-Pierre Henry  Adam Parusiński
Institution:(1) Centre de Mathématiques, (Unité associé au CNRS No169), Ecole Polytechnique, F-91128 Palaiseau Cedex, France;(2) Département de Mathématiques, Université d'Angers, 2, bd Lavoisier, 49045 Angers Cedex 1, France
Abstract:We show that the bi-Lipschitz equivalence of analytic function germs (Copf2, 0)rarr(Copf, 0) admits continuous moduli. More precisely, we propose an invariant of the bi-Lipschitz equivalence of such germs that varies continuously in many analytic families f t : (Copf2, 0)rarr(Copf, 0). For a single germ f the invariant of f is given in terms of the leading coefficients of the asymptotic expansions of f along the branches of generic polar curve of f.
Keywords:analytic function germs  bi-Lipschitz equivalence  moduli  polar curve  Newton polygon
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