Work

Generalized Dimensions of Self-Affine Sets with Overlaps

Year: 2024

Type: article

Abstract: Two decades ago, Ngai and Wang introduced a well-known finite type condition (FTC) on the self-similar iterated function system (IFS) with overlaps and used it to calculate the Hausdorff dimension of self-similar sets. In this paper, inspired by Ngai and Wang’s idea, we define a new FTC on self-affine IFS and obtain an analogous formula on the generalized dimensions of self-affine sets. The generalized dimensions raised by He and Lau are used to estimate the Hausdorff dimension of self-affine sets.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract8120722

Authors: Guanzhong Ma, Jun Luo, Xiao Zhou

Institutions: Anyang Normal University, Chongqing University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,069

Funder: Natural Science Foundation of Chongqing