Fixed points and dynamics of holomorphic maps

TL;DR

This paper reviews the known results on local and global dynamics of holomorphic maps near fixed points in one and multiple complex variables, highlighting their mathematical properties and implications.

Contribution

It provides a systematic review of existing results on holomorphic fixed points and their dynamics, integrating local and global perspectives.

Findings

Summary of local dynamics near fixed points

Implications for global dynamics of holomorphic maps

Connections between fixed point behavior and overall system dynamics

Abstract

In this manuscript we systematically review known results of local dynamics of discrete local holomorphic dynamics near fixed points in one and several complex variables as well as the consequences in global dynamics.