Holomorphic dynamics near germs of singular curves
Abstract
Let M be a two dimensional complex manifold, p ∈ M and a germ of holomorphic foliation of at p. Let S⊂ M be a germ of an irreducible, possibly singular, curve at p in M which is a separatrix for . We prove that if the Camacho-Sad-Suwa index (,S,p) ∈ + \0\ then there exists another separatrix for at p. A similar result is proved for the existence of parabolic curves for germs of holomorphic diffeomorphisms near a curve of fixed points.
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