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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.04875 |
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| _version_ | 1866911200124600320 |
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| author | Allen, Demi Jordan, Thomas Ward, Benjamin |
| author_facet | Allen, Demi Jordan, Thomas Ward, Benjamin |
| contents | Since the introduction of the shrinking target problem by Hill and Velani in 1995 there has been a surge of interest in the area. In this paper we consider the case where the target is a rectangle, rather than a ball, and the underlying space is a self-similar carpet. We calculate the exact Hausdorff dimension of the resulting shrinking target set. Interestingly the Hausdorff dimension depends on the centre of the target, a condition uncommon in most other shrinking target type problems. This extends a theorem of Wang and Wu [Theorem 12.1, Math. Ann. 2021]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04875 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rectangular Shrinking Targets on Self-Similar Carpets Allen, Demi Jordan, Thomas Ward, Benjamin Dynamical Systems 37C45, 28A80 Since the introduction of the shrinking target problem by Hill and Velani in 1995 there has been a surge of interest in the area. In this paper we consider the case where the target is a rectangle, rather than a ball, and the underlying space is a self-similar carpet. We calculate the exact Hausdorff dimension of the resulting shrinking target set. Interestingly the Hausdorff dimension depends on the centre of the target, a condition uncommon in most other shrinking target type problems. This extends a theorem of Wang and Wu [Theorem 12.1, Math. Ann. 2021]. |
| title | Rectangular Shrinking Targets on Self-Similar Carpets |
| topic | Dynamical Systems 37C45, 28A80 |
| url | https://arxiv.org/abs/2510.04875 |