Invariants of bi-Lipschitz equivalence of real analytic functions

• Autorzy: Jean-Pierre Henry , Adam Parusiński
• Języki publikacji: EN

Abstrakty

EN

We construct an invariant of the bi-Lipschitz equivalence of analytic function germs (ℝⁿ,0) → (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)|.

Kategorie tematyczne

• 32S05: Local singularities
• 32S15: Equisingularity (topological and analytic)
• 14H15: Families, moduli (analytic)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2004
• Tom: 65
• Numer: 1
• Strony: 67-75

Daty

wydano

2004

Twórcy

autor

Jean-Pierre Henry

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

autor

Adam Parusiński

• Département de Mathématiques, U.M.R. 6093 du C.N.R.S, Université d'Angers, 2, bd Lavoisier, 49045 Angers Cedex, France

Identyfikatory

DOI

10.4064/bc65-0-5