The dimension spectrum of the infinitely generated Apollonian gasket
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916707202760704 |
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| author | Chousionis, Vasileios Leykekhman, Dmitriy Urbański, Mariusz Wendt, Erik |
| author_facet | Chousionis, Vasileios Leykekhman, Dmitriy Urbański, Mariusz Wendt, Erik |
| contents | We prove that the infinitely generated Apollonian gasket has full Hausdorff dimension spectrum. Our proof, which is computer assisted, relies on an iterative technique introduced by the first three authors in [3] and on a flexible method for rigorously estimating Hausdorff dimensions of limit sets of conformal iterated function systems, which we recently developed in [5]. Another key ingredient in our proof is obtaining reasonably sized distortion constants for the (infinite) Apollonian iterated function system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17835 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The dimension spectrum of the infinitely generated Apollonian gasket Chousionis, Vasileios Leykekhman, Dmitriy Urbański, Mariusz Wendt, Erik Dynamical Systems 37D35, 37C30, 28A80, 52C26 We prove that the infinitely generated Apollonian gasket has full Hausdorff dimension spectrum. Our proof, which is computer assisted, relies on an iterative technique introduced by the first three authors in [3] and on a flexible method for rigorously estimating Hausdorff dimensions of limit sets of conformal iterated function systems, which we recently developed in [5]. Another key ingredient in our proof is obtaining reasonably sized distortion constants for the (infinite) Apollonian iterated function system. |
| title | The dimension spectrum of the infinitely generated Apollonian gasket |
| topic | Dynamical Systems 37D35, 37C30, 28A80, 52C26 |
| url | https://arxiv.org/abs/2504.17835 |