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1 results

  • Existence of Moduli for Bi-Lipschitz Equivalence of Analytic Functions

  • Jean-Pierre Henry, Adam Parusiński
  • Journal:
    Compositio Mathematica / Volume 136 / Issue 2 / April 2003
    Published online by Cambridge University Press:
    04 December 2007, pp. 217-235
    Print publication:
    April 2003
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  • We show that the bi-Lipschitz equivalence of analytic function germs (${\open C}^{2}$, 0)→(${\open C}$, 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 ft: (${\open C}^{2}$, 0)→(${\open C}$, 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.