Prépublication n° 147
We construct an invariant of the bi-Lipschitz equivalence of analytic function germs $(\R^n,0)\to (\R,0)$ that varies continuously in many analytic families. This shows that the bi-Lipschitz equivalence of analytic function germs admits continuous moduli. For a germ $f$ the invariant is given in terms of the leading coefficients of the asymptotic expansions of $f$ along the sets where the size of $|x||grad \, f(x)|$ is comparable to the size of $|f(x)|$.
32S05 Local singularities [See also 14J17]
14H15 Families, moduli (analytic) [See also 30F10, 32Gxx]
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