Box dimension of fractal functions on attractors
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913530731560960 |
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| author | Pasupathi, R. |
| author_facet | Pasupathi, R. |
| contents | We study a wide class of fractal interpolation functions in a single platform by considering the domains of these functions as general attractors. We obtain lower and upper bounds of the box dimension of these functions in a more general setup where the interpolation points need not be equally spaced, the scale vectors can be variables and the maps in the corresponding IFS can be non-affine. In particular, we obtain the exact value of the box dimension of non-affine fractal functions on general m-dimensional cubes and Sierpinski Gasket. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_03144 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Box dimension of fractal functions on attractors Pasupathi, R. Dynamical Systems Metric Geometry 28A80, 41A05, 37E05 We study a wide class of fractal interpolation functions in a single platform by considering the domains of these functions as general attractors. We obtain lower and upper bounds of the box dimension of these functions in a more general setup where the interpolation points need not be equally spaced, the scale vectors can be variables and the maps in the corresponding IFS can be non-affine. In particular, we obtain the exact value of the box dimension of non-affine fractal functions on general m-dimensional cubes and Sierpinski Gasket. |
| title | Box dimension of fractal functions on attractors |
| topic | Dynamical Systems Metric Geometry 28A80, 41A05, 37E05 |
| url | https://arxiv.org/abs/2410.03144 |