Invariants of bi-Lipschitz equivalence of real analytic functions
Volume 65 / 2004
Banach Center Publications 65 (2004), 67-75
MSC: 32S15, 32S05, 14H15.
DOI: 10.4064/bc65-0-5
Abstract
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 $|f(x)|$.
