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 |
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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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