Hedgehogs in higher dimensions and their applications
  In this paper we study the dynamics of germs of holomorphic diffeomorphisms of $(\mathbb{C}^{n},0)$ with a fixed point at the origin with exactly one neutral eigenvalue. We prove that the map on any local center manifold of $0$ is quasiconformally conjugate to a holomorphic map and use this to transport results from one complex dimension to higher dimensions. 
Mikhail Lyubich, Remus Radu, and Raluca Tanase
math.DS math.CV