Work

Box dimension of the graphs of recurrent fractal interpolation functions

Year: 2026

Type: article

Abstract: Let f be a generalized affine recurrent fractal interpolation function with vertical scaling functions. In this paper, by introducing underlying local iterated function systems of f , we define restricted vertical scaling matrices. Then we analyze the irreducibility and monotonicity of spectral radii of these matrices. With these matrices, we study the oscillation sums of f . As a result, we estimate the box dimension of the graph of f by the limits of spectral radii of these matrices. In particular, we obtain an explicit formula of the box dimension of the graph of f under certain constraint conditions.

Source: Nonlinearity

DOI: 10.1088/1361-6544/ae9de2

Authors: Lai Jiang, Xiao-Hui Li, Zhen Liang, Huo-Jun Ruan

Institutions: University of Chinese Academy of Sciences, Yantai University, Nanjing Audit University, Zhejiang University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Fundamental Research Funds for the Central Universities

Awards: G1163496811, G5178879198