The Hausdorff dimension of directional edge escaping points set

Huang, Xiaojie; Liu, Zhixiu; Li, Yuntong

doi:10.3336/gm.57.2.05

Glasnik matematički, Vol. 57 No. 2, 2022.

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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APA 6th Edition

Huang, X., Liu, Z. & Li, Y. (2022). The Hausdorff dimension of directional edge escaping points set. Glasnik matematički, 57 (2), 239-250. https://doi.org/10.3336/gm.57.2.05

MLA 8th Edition

Huang, Xiaojie, et al. "The Hausdorff dimension of directional edge escaping points set." Glasnik matematički, vol. 57, no. 2, 2022, pp. 239-250. https://doi.org/10.3336/gm.57.2.05. Accessed 23 Jun. 2024.

Chicago 17th Edition

Huang, Xiaojie, Zhixiu Liu and Yuntong Li. "The Hausdorff dimension of directional edge escaping points set." Glasnik matematički 57, no. 2 (2022): 239-250. https://doi.org/10.3336/gm.57.2.05

Harvard

Huang, X., Liu, Z., and Li, Y. (2022). 'The Hausdorff dimension of directional edge escaping points set', Glasnik matematički, 57(2), pp. 239-250. https://doi.org/10.3336/gm.57.2.05

Vancouver

Huang X, Liu Z, Li Y. The Hausdorff dimension of directional edge escaping points set. Glasnik matematički [Internet]. 2022 [cited 2024 June 23];57(2):239-250. https://doi.org/10.3336/gm.57.2.05

IEEE

X. Huang, Z. Liu and Y. Li, "The Hausdorff dimension of directional edge escaping points set", Glasnik matematički, vol.57, no. 2, pp. 239-250, 2022. [Online]. https://doi.org/10.3336/gm.57.2.05

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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.