Bilipschitz invariants for germs of holomorphic foliations

Abstract

In this paper we study bilipschitz equivalences of germs of holomorphic foliations in $({\mathbb{C}}^2,0)$. We prove that the algebraic multiplicity of a singularity is invariant by such equivalences. Moreover, for a large class of singularities, we show that the projective holonomy representation is also a bilipschitz invariant.