The Exponential Map Is Chaotic: An Invitation to Transcendental Dynamics



Shen, Zhaiming and Rempe-Gillen, Lasse ORCID: 0000-0001-8032-8580
(2015) The Exponential Map Is Chaotic: An Invitation to Transcendental Dynamics. AMERICAN MATHEMATICAL MONTHLY, 122 (10). pp. 919-940.

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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.

Item Type: Article
Additional Information: 22 pages, 4 figures. (Provisionally) accepted for publication the American Mathematical Monthly. V2: Final pre-publication version. The article has been revised, corrected and shortened by 14 pages; see Version 1 for a more detailed discussion of further properties of the exponential map and wider transcendental dynamics
Uncontrolled Keywords: math.DS, math.DS, math.CV, 37F10, 30D05
Depositing User: Symplectic Admin
Date Deposited: 15 Jul 2015 10:08
Last Modified: 15 Dec 2022 23:31
DOI: 10.4169/amer.math.monthly.122.10.919
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/2015779

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