Homotopy Hubbard Trees for Post-Singularly Finite Transcendental Entire Maps
Homotopy Hubbard Trees for Post-Singularly Finite Transcendental Entire Maps
复制标题
后奇异有限先验全图的同伦哈伯德树
DOI：
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
David Pfrang
中科院分区：
文献类型：
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作者：
David Pfrang
该项目的主要目标是研究在多项式动力学中广泛使用的哈伯德树概念对于超越整个函数是否也有意义。
对于后临界有限多项式，其哈伯德树是唯一的最小嵌入树，包含所有临界点，并且在多项式的动态下具有前向不变性（并且在某种意义上，在 Fatou 分量上标准化）。使这个定义适应后奇异有限（psf）超越整个映射并不困难。然而，我们表明存在 psf 整个地图不允许哈伯德树。其原因是渐近值的存在。
部分为了解决这个问题，我们引入了同伦哈伯德树的概念。与哈伯德树的本质区别在于，同伦哈伯德树仅需要相对于后奇异集具有前向不变性直至同伦。我们在这项工作中的主要成就是证明每个 psf 超越整个映射都承认同伦哈伯德树，并且该树相对于后奇异集的同伦是唯一的。
作为根据同伦哈伯德树对 psf 整个函数进行分类的第一步，我们表明映射是由其树唯一确定的。
The main goal of this project is to investigate whether the concept of a Hubbard Tree, well established and widely used in polynomial dynamics, is also meaningful for transcendental entire functions.
For a post-critically finite polynomial, its Hubbard Tree is the unique minimal embedded tree that contains all critical points and is forward invariant under the dynamics of the polynomial (and, in a certain sense, normalized on Fatou components). It is not difficult to adapt this definition to post-singularly finite (psf) transcendental entire maps. We show, however, that there are psf entire maps that do not admit a Hubbard Tree. The reason for this is the existence of asymptotic values.
Partly in order to deal with that issue, we introduce the concept of a Homotopy Hubbard Tree. The essential difference to a Hubbard Tree is that a Homotopy Hubbard Tree is only required to be forward invariant up to homotopy relative to the post-singular set. Our main accomplishment in this work is to show that every psf transcendental entire map admits a Homotopy Hubbard Tree and that this tree is unique up to homotopy relative to the post-singular set.
As a first step towards a classification of psf entire functions in terms of Homotopy Hubbard Trees, we show that a map is uniquely determined by its tree.
DOI：
10.48550/arxiv.1101.4209
发表时间：
2011
期刊：
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影响因子：
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作者：
Baranski K
通讯作者：
Baranski K
后奇异有限指数映射的同伦哈伯德树
影响因子：
0.9
作者：
David Pfrang;Michael Rothgang;Dierk Schleicher
通讯作者：
Dierk Schleicher