arXiv:1506.07113 Abstract | arXiv Analytics

arXiv:1506.07113 [math.DS]Abstract References Reviews Resources

Around the boundary of complex dynamics

Published 2015-06-23Version 1

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.

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. 56 pages and 25 figures

Categories: math.DS, math.CV

Keywords: complex dynamics, typical first course, complex analysis, undergraduate level, julia sets

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