Holomorphic flows in C3, 0 with resonancese

Abstract

The topological classification, by conjugacy, of the germs of holomorphic diffeomorphisms f: C2, 0 →C2, 0 with df(0) = diag(λ1, λ2), where λ1 is a root of unity and | λ2 | ≠ 1 is given. This type of diffeomorphism appears as holonomies of singular foliations Fx induced by holomorphic vector fields X: C3, 0 → C3, 0 normally hyperbolic and resonant. An explicit example of a such vector field without holomorphic invariant center manifold is presented. We prove that there are no obstructions in the holonomies for Fx to be topologically equivalent to a product type foliation. © 1992 American Mathematical Society.