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# Wydawnictwa / Banach Center Publications / Wszystkie tomy

## Invariants of bi-Lipschitz equivalence of real analytic functions

### Tom 65 / 2004

Banach Center Publications 65 (2004), 67-75 MSC: 32S15, 32S05, 14H15. DOI: 10.4064/bc65-0-5

#### Streszczenie

We construct an invariant of the bi-Lipschitz equivalence of analytic function germs $(\mathbb R^n,0)\to (\mathbb R,0)$ 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 $|x|\,|{\mathop{\rm grad} f(x)}|$ is comparable to the size of $|f(x)|$.

#### Autorzy

• Jean-Pierre HenryCentre de Mathématiques
(Unité associé au CNRS no. 169)
École Polytechnique
F-91128 Palaiseau Cedex, France
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