Tangents of invariant sets
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914984861106176 |
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| author | Käenmäki, Antti Rutar, Alex |
| author_facet | Käenmäki, Antti Rutar, Alex |
| contents | We study the fine scaling properties of sets satisfying various weak forms of invariance. For general attractors of possibly overlapping bi-Lipschitz iterated function systems, we establish that the Assouad dimension is given by the Hausdorff dimension of a tangent at some point in the attractor. Under the additional assumption of self-conformality, we moreover prove that this property holds for a subset of full Hausdorff dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_11971 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tangents of invariant sets Käenmäki, Antti Rutar, Alex Dynamical Systems Classical Analysis and ODEs Metric Geometry 28A80 (Primary) 37C45, 28A78 (Secondary) We study the fine scaling properties of sets satisfying various weak forms of invariance. For general attractors of possibly overlapping bi-Lipschitz iterated function systems, we establish that the Assouad dimension is given by the Hausdorff dimension of a tangent at some point in the attractor. Under the additional assumption of self-conformality, we moreover prove that this property holds for a subset of full Hausdorff dimension. |
| title | Tangents of invariant sets |
| topic | Dynamical Systems Classical Analysis and ODEs Metric Geometry 28A80 (Primary) 37C45, 28A78 (Secondary) |
| url | https://arxiv.org/abs/2309.11971 |