Around the boundary of complex dynamics
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.
Keywords
Cite
@article{arxiv.1506.07113,
title = {Around the boundary of complex dynamics},
author = {Roland K. W. Roeder},
journal= {arXiv preprint arXiv:1506.07113},
year = {2015}
}
Comments
These notes were written for the 2015 Thematic Program on Boundaries and Dynamics held at Notre Dame University. They are intended for an advanced undergraduate student who is majoring in mathematics. 57 pages and 25 figures. Version 2: some typos fixed and references added