A Discrete Version of Local Hausdorff Dimension on Infinite Fractal Networks
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.
Authors
- Daohua Wang (ORCID: https://orcid.org/0009-0006-1270-3805)
- Cheng Zeng (ORCID: https://orcid.org/0000-0002-8810-0844)
- Zixuan Zhao (ORCID: https://orcid.org/0009-0007-1624-1510)
Institutions
- Xidian University (CN)
- Beihang University (CN)
- Shandong Institute of Business and Technology (CN)
Publication Details
- Journal
- Axioms
- Published
- 2026-05-27
- DOI
- https://doi.org/10.3390/axioms15060402
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Natural Science Foundation of China