Box dimension of the graphs of recurrent fractal interpolation functions
Classical Analysis and ODEs
2025-10-06 v1
Abstract
Let be a generalized affine recurrent fractal interpolation function with vertical scaling functions. In this paper, by introducing underlying local iterated function systems of , we define restricted vertical scaling matrices. Then we prove the monotonicity of spectral radii of these matrices without additional conditions. We also prove the irreducibility of these matrices under the assumption that vertical scaling functions are positive. With these results, we estimate the upper and lower box dimensions of the graphs of by the limits of spectral radii of restricted vertical scaling matrices. In particular, we obtain an explicit formula of the box dimension of the graph of under certain constraint conditions.
Keywords
Cite
@article{arxiv.2510.02754,
title = {Box dimension of the graphs of recurrent fractal interpolation functions},
author = {Lai Jiang and Xiao-Hui Li and Zhen Liang and Huo-Jun Ruan},
journal= {arXiv preprint arXiv:2510.02754},
year = {2025}
}