方向边转义点集的Hausdorff维数

Pub Date : 2022-12-30 DOI:10.3336/gm.57.2.05

Xiaojie Huang, Zhixiu Liu, Yuntong Li

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引用次数: 0

摘要

本文定义了给定平面划分下函数迭代的方向边转义点集，并证明了\(S(z)=a e^{z}+b e^{-z}\)的方向边转义点集的Hausdorff维数上界不大于1，其中\(a, b\in \mathbb{C}\)和\(|a|^{2}+|b|^{2}\neq 0\)。

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The Hausdorff dimension of directional edge escaping points set

In this paper, we define the directional edge escaping points set of function iteration under a given plane partition and then prove that the upper bound of Hausdorff dimension of the directional edge escaping points set of \(S(z)=a e^{z}+b e^{-z}\), where \(a, b\in \mathbb{C}\) and \(|a|^{2}+|b|^{2}\neq 0\), is no more than 1.

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