The Exponential Map Is Chaotic: An Invitation to Transcendental Dynamics

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 i...

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Veröffentlicht in:	The American mathematical monthly 2015-12, Vol.122 (10), p.919-940
Hauptverfasser:	Shen, Zhaiming, Rempe-Gillen, Lasse
Format:	Artikel
Sprache:	eng
Schlagworte:	Chaos theory Complex analysis Curricula Distance functions Dynamical systems Exponential functions Geometric planes Hyperbolic geometry Infinity Mathematical constants Mathematical theorems Mathematics Topological theorems
Online-Zugang:	Volltext
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