Original scientific paper

https://doi.org/10.3336/gm.57.2.05

The Hausdorff dimension of directional edge escaping points set

Xiaojie Huang ; Department of Science, Nanchang Institute of Technology, 330099 Nanchang, China
Zhixiu Liu ; Department of Science, Nanchang Institute of Technology, 330099 Nanchang, China
Yuntong Li ; Department of Basic Courses, Shaanxi Railway Institute, 714000 Weinan, China

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Abstract

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.

Keywords

Directional edge escaping points set, plane partition, function iteration, exponential function, Hausdorff dimension

Hrčak ID:

289605

URI

https://hrcak.srce.hr/289605

Publication date:

30.12.2022.

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