Box dimension of the graphs of recurrent fractal interpolation functions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914072537071616 |
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| author | Jiang, Lai Li, Xiao-Hui Liang, Zhen Ruan, Huo-Jun |
| author_facet | Jiang, Lai Li, Xiao-Hui Liang, Zhen Ruan, Huo-Jun |
| contents | 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 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 $f$ 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 $f$ under certain constraint conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02754 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Box dimension of the graphs of recurrent fractal interpolation functions Jiang, Lai Li, Xiao-Hui Liang, Zhen Ruan, Huo-Jun Classical Analysis and ODEs 28A80, 41A30 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 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 $f$ 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 $f$ under certain constraint conditions. |
| title | Box dimension of the graphs of recurrent fractal interpolation functions |
| topic | Classical Analysis and ODEs 28A80, 41A30 |
| url | https://arxiv.org/abs/2510.02754 |