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A Discrete Version of Local Hausdorff Dimension on Infinite Fractal Networks | Synapse

May 29, 2026Axioms0 citationsOpen Access

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A Discrete Version of Local Hausdorff Dimension on Infinite Fractal Networks

CZCheng Zeng DWDaohua Wang ZZZixuan Zhao

Key Points

The paper aims to define and analyze the local Hausdorff dimension on infinite fractal networks and explore its properties.
Defined local Hausdorff dimension based on α-potential at a point x in Rd.
Proved basic properties and calculated local Hausdorff dimensions of specific networks.
Introduced a generalized definition of subset Hausdorff dimension.
Established fundamental properties of local Hausdorff dimension.
Calculated the local Hausdorff dimension for specific fractal networks.
Presented a broad definition through subset Hausdorff dimension.

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.

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Cite This Study

Zeng et al. (Wed,) studied this question.

synapsesocial.com/papers/6a192d4afab5b468c44161e5 https://doi.org/https://doi.org/10.3390/axioms15060402