Henry, Jean-Pierre; Parusiński, Adam Existence of moduli for bi-Lipschitz equivalence of analytic functions. (English) Zbl 1026.32055 Compos. Math. 136, No. 2, 217-235 (2003). Let \(f_t(x,y) = x^3 - 3t^2 x y^4 + y^6\) define a one parameter family of germs \(f_t : (\mathbb{C}^2,0) \to (\mathbb{C},0)\), \(t \in \mathbb{C}\). It is proved that if \(t,t^\prime\) are sufficiently generic, then \(f_t\) and \(f_{t^\prime}\) are not bi-Lipschitz equivalent function germs, that is, there is no germ of bi-Lipschitz homeomorphism \(H : (\mathbb{C}^2,0) \to (\mathbb{C}^2,0)\) such that \(f_t \circ H = f_{t^\prime}\). Reviewer: Gerhard Pfister (Kaiserslautern) Cited in 2 ReviewsCited in 17 Documents MSC: 32S05 Local complex singularities 14H15 Families, moduli of curves (analytic) 32S15 Equisingularity (topological and analytic) Keywords:analytic function germs; bi-Lipschitz equivalence; Newton polygon PDFBibTeX XMLCite \textit{J.-P. Henry} and \textit{A. Parusiński}, Compos. Math. 136, No. 2, 217--235 (2003; Zbl 1026.32055) Full Text: DOI