LAREMA Prépublication n° 147

### Invariants of Bi-Lipschitz Equivalence of Real Analytic Functions

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 $|f(x)|$.

Mots Clés
Bi-lipschitz equivalence ; characteristic exponents ; polar curves

Codes MSC