Discrete holomorphic local dynamical systems

TL;DR

This survey reviews the local dynamics of holomorphic maps in complex variables, focusing on normal forms, stable sets, and recent developments, providing comprehensive proofs and an extensive bibliography.

Contribution

It updates and expands previous surveys by including new results, proofs, and a broader bibliography on local holomorphic dynamical systems.

Findings

Analysis of normal forms for holomorphic maps

Structure of local stable sets in non-hyperbolic cases

Compilation of recent proofs and extensive references

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.