The exponential map is chaotic: An invitation to transcendental dynamics
Dynamical Systems
2020-08-26 v2 Complex Variables
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.
Keywords
Cite
@article{arxiv.1408.1129,
title = {The exponential map is chaotic: An invitation to transcendental dynamics},
author = {Zhaiming Shen and Lasse Rempe-Gillen},
journal= {arXiv preprint arXiv:1408.1129},
year = {2020}
}
Comments
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