无限维瑟斯顿理论与先验动力学I:无限腿蜘蛛

IF 0.5 3区 数学 Q3 MATHEMATICS
K. Bogdanov
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引用次数: 3

摘要

我们开发了一种技术,为著名的Thurston有理函数的拓扑表征的推广奠定了基础,该表征适用于无限次的标记点和分支覆盖的无限集。与经典定理类似,我们考虑瑟斯顿映射作用于泰希姆乌勒空间,这一次是无限维的,这导致了一个完全不同的理论,与经典的设置相比。我们通过给出Markus F\ \ orster关于带转义奇异值的指数函数分类结果的另一种证明来证明我们的技术。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Infinite-dimensional Thurston theory and transcendental dynamics I: infinite-legged spiders
We develop techniques that lay out a basis for generalizations of the famous Thurston's Topological Characterization of Rational Functions for an infinite set of marked points and branched coverings of infinite degree. Analogously to the classical theorem we consider the Thurston's $\sigma$-map acting on a Teichm\"uller space which is this time infinite-dimensional -- and this leads to a completely different theory comparing to the classical setting. We demonstrate our techniques by giving an alternative proof of the result by Markus F\"orster about the classification of exponential functions with the escaping singular value.
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来源期刊
Fundamenta Mathematicae
Fundamenta Mathematicae 数学-数学
CiteScore
1.00
自引率
0.00%
发文量
44
审稿时长
6-12 weeks
期刊介绍: FUNDAMENTA MATHEMATICAE concentrates on papers devoted to Set Theory, Mathematical Logic and Foundations of Mathematics, Topology and its Interactions with Algebra, Dynamical Systems.
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