Work

A Discrete Version of Local Hausdorff Dimension on Infinite Fractal Networks

Year: 2026

Type: article

Abstract: In this paper, we define the local Hausdorff dimension on fractal networks inspired by the idea of α-potential at a point x∈Rd. We prove some basic properties of the local Hausdorff dimension and then obtain the local Hausdorff dimension of some networks. We also discuss a more generalized dimension definition, namely the subset Hausdorff dimension.

Source: Axioms

DOI: 10.3390/axioms15060402

Authors: Cheng Zeng, Daohua Wang, Zixuan Zhao

Institutions: Shandong Institute of Business and Technology, Xidian University, Beihang University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: National Natural Science Foundation of China