Fractal tiles induced by tent maps
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917006010220544 |
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| author | Scheicher, Klaus Sirvent, Victor F. Surer, Paul |
| author_facet | Scheicher, Klaus Sirvent, Victor F. Surer, Paul |
| contents | In the present article, we deal with geometrical objects induced by the tent maps associated with special Pisot numbers that we call tent-tiles. They are compact subsets of the one-, two-, or three-dimensional Euclidean space, depending on the particular special Pisot number. Most of the tent-tiles have a fractal shape and we study the Hausdorff dimension of their boundary. Furthermore, we are concerned with tilings induced by tent-tiles. It turns out that tent-tiles give rise to two types of lattice tilings. In order to obtain these results we establish and exploit connections between tent-tiles and Rauzy fractals induced by substitutions and automorphisms of the free group. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_16790 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractal tiles induced by tent maps Scheicher, Klaus Sirvent, Victor F. Surer, Paul Dynamical Systems 37B10, 11R06, 28A78, 37E05, 28A80 In the present article, we deal with geometrical objects induced by the tent maps associated with special Pisot numbers that we call tent-tiles. They are compact subsets of the one-, two-, or three-dimensional Euclidean space, depending on the particular special Pisot number. Most of the tent-tiles have a fractal shape and we study the Hausdorff dimension of their boundary. Furthermore, we are concerned with tilings induced by tent-tiles. It turns out that tent-tiles give rise to two types of lattice tilings. In order to obtain these results we establish and exploit connections between tent-tiles and Rauzy fractals induced by substitutions and automorphisms of the free group. |
| title | Fractal tiles induced by tent maps |
| topic | Dynamical Systems 37B10, 11R06, 28A78, 37E05, 28A80 |
| url | https://arxiv.org/abs/2503.16790 |