Rectangular shrinking targets on self-similar carpets
Abstract
Abstract 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].
Fields of Study & Subjects
Fluid Dynamics Simulations and Interactions
Computational Geometry and Mesh Generation
Publication details
- Journal / source
- International Mathematics Research Notices
- Volume
- 2026
- Issue
- 10
- Publication date
- 17 April 2026
- Language
- EN