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arXiv · 1408.1129

The exponential map is chaotic: An invitation to transcendental dynamics

Zhaiming Shen·Lasse Rempe-Gillen
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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 result 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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Zhaiming Shen, Lasse Rempe-Gillen. 2014-08-05. The exponential map is chaotic: An invitation to transcendental dynamics. https://doi.org/10.4169/amer.math.monthly.122.10.919

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