Tangent measures of self-similar sets satisfying the strong separation condition
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910056204730368 |
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| author | Wang, Yongtao |
| author_facet | Wang, Yongtao |
| contents | This paper investigates tangent measures in the sense of Preiss for self-similar sets on ${\mathbb{R}^d}$ that satisfy the strong separation condition. Through the dynamics of ``zooming in'' on any typical point, we derive an explicit and uniform formula for the tangent measures associated with this category of self-similar sets on ${\mathbb{R}^d}$. Furthermore, for any self-similar set $C\subset{\mathbb{R}^d}$ under the open set condition instead of the strong separation condition, we find that the support of any tangent measure at each point $x\in C$ is one of the limit models at that point. Conversely, any limit model at each point $x\in C$ is the support of one of the tangent measures at that point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16467 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tangent measures of self-similar sets satisfying the strong separation condition Wang, Yongtao Dynamical Systems 28A33, 28A78, 28A80 This paper investigates tangent measures in the sense of Preiss for self-similar sets on ${\mathbb{R}^d}$ that satisfy the strong separation condition. Through the dynamics of ``zooming in'' on any typical point, we derive an explicit and uniform formula for the tangent measures associated with this category of self-similar sets on ${\mathbb{R}^d}$. Furthermore, for any self-similar set $C\subset{\mathbb{R}^d}$ under the open set condition instead of the strong separation condition, we find that the support of any tangent measure at each point $x\in C$ is one of the limit models at that point. Conversely, any limit model at each point $x\in C$ is the support of one of the tangent measures at that point. |
| title | Tangent measures of self-similar sets satisfying the strong separation condition |
| topic | Dynamical Systems 28A33, 28A78, 28A80 |
| url | https://arxiv.org/abs/2603.16467 |