指数映射是混沌的：超越动力学导论
动力系统
2020-08-26 v2 复变函数
摘要
我们给出了一个初等的、概念性的证明，表明复指数映射在作为复平面上的动力系统时是'混沌的'。（这一结果由 Fatou 于 1926 年猜想，55 年后由 Misiurewicz 首次证明。）所需背景仅为复分析的第一门本科课程。
引用
@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}
}
备注
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