Discrete holomorphic local dynamical systems
arXiv:0903.3289
Abstract
This is a survey on local dynamics of holomorphic maps in one and several complex variables, discussing in particular normal forms and the structure of local stable sets in the non-hyperbolic case, and including several proofs and a vast bibliography. It updates and enlarge the previous survey arXiv:math/0310089v1.
Notes of the CIME course given in Cetraro (Italy) in July 2008. To appear in "Holomorphic dynamics", G.Gentili, J. Guenot, G. Patrizio eds., Lect. Notes in Math., Springer, Berlin, 2009