Hedgehogs for neutral dissipative germs of holomorphic diffeomorphisms of $({\mathbb{C}}^2,0)$

Abstract

We prove the existence of hedgehogs for germs of complex analytic diffeomorphisms of $({\mathbb{C}}^2,0)$ with a semi-neutral fixed point at the origin, using topological techniques. This approach also provides an alternative proof of a theorem of Pérez-Marco on the existence of hedgehogs for germs of univalent holomorphic maps of $(\mathbb{C},0)$ with a neutral fixed point.