On the Dynamics of Complex Quadratic Families under Holomorphic and Non-Holomorphic Singular Perturbations

TL;DR

This paper explores how complex quadratic maps behave under different types of singular perturbations, analyzing their topological and statistical properties to understand their dynamics.

Contribution

It provides a comprehensive survey of the effects of holomorphic and non-holomorphic perturbations on complex quadratic maps, highlighting new insights into their dynamics.

Findings

Topological properties of perturbed quadratic maps analyzed

Statistical behaviors under different perturbations characterized

Differences between holomorphic and non-holomorphic effects identified

Abstract

This work surveys the topological and statistical properties of real quadratic maps and investigates the complex quadratic maps under holomorphic and non-holomorphic singular perturbations.