Discrete local holomorphic dynamics

Let M be a complex manifold, and p ∈ M. In this survey, a (discrete) holomorphic local dynamical system at p will be a holomorphic map f: U → M such that f(p) = p, where U ⊆ M is an open neighbourhood of p; we shall also assume that f ̸ ≡ idU. We shall denote by End(M, p) the set of holomorphic local dynamical systems at p.