Existence of Moduli for Bi-Lipschitz Equivalence of Analytic Functions |
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Authors: | Jean-Pierre Henry Adam Parusiński |
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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 |
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Abstract: | We show that the bi-Lipschitz equivalence of analytic function germs (2, 0)(, 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
: (2, 0)(, 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. |
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Keywords: | analytic function germs bi-Lipschitz equivalence moduli polar curve Newton polygon |
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