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Abstract
We present an elementary and conceptual proof that the complex exponential map is chaotic when considered as a dynamical system on the complex plane. (This was conjectured by Fatou in 1926 and first proved by Misiurewicz 55 years later.) The only background required is a first undergraduate course in complex analysis.
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Notes on contributors
Zhaiming Shen
ZHAIMING SHEN studied mathematics at Xi′an Jiaotong-Liverpool University in Suzhou (China) and at the University of Liverpool (UK). He received his BSc in 2014 and is now a doctoral student at the University of Pennsylvania.
Lasse Rempe-Gillen
LASSE REMPE-GILLEN is professor of pure mathematics at the University of Liverpool (UK). Having studied mathematics and computer science in Kiel (Germany), Stony Brook (USA), Paris (France), and Warwick (UK), he received his doctoral degree in 2003 from the University of Kiel. His research, which focuses on the dynamics of functions of one complex variable, was awarded a Whitehad Prize in 2010, a Philip Leverhulme Prize in 2012, and the CMFT Young Researcher Award in 2013.