Around the boundary of complex dynamics

TL;DR

This paper introduces complex dynamics at an undergraduate level, covering Julia and Mandelbrot sets, their boundary properties, and applications to astrophysics, aiming to bridge foundational concepts with advanced interdisciplinary problems.

Contribution

It provides an accessible introduction to complex dynamics, emphasizing boundary properties and interdisciplinary applications, extending typical undergraduate curricula.

Findings

Properties of Julia and Mandelbrot set boundaries explained

Connections between complex dynamics and astrophysics discussed

Educational approach for undergraduate learning emphasized

Abstract

We introduce the exciting field of complex dynamics at an undergraduate level while reviewing, reinforcing, and extending the ideas learned in an typical first course on complex analysis. Julia sets and the famous Mandelbrot set will be introduced and interesting properties of their boundaries will be described. We will conclude with a discussion of problems at the boundary between complex dynamics and other areas, including a nice application of the material we have learned to a problem in astrophysics.