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Genericity of dimension drop on self-affine sets
We prove that generically, for a self-affine set in \(\mathbb{R}^d\), removing one of the affine maps which defines the set results in a strict reduction of the Hausdorff dimension. This gives a partial positive answer to a folklore open question.
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| Published in: | arXiv.org 2017-03 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Online Access: | Get full text |
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| Summary: | We prove that generically, for a self-affine set in \(\mathbb{R}^d\), removing one of the affine maps which defines the set results in a strict reduction of the Hausdorff dimension. This gives a partial positive answer to a folklore open question. |
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| ISSN: | 2331-8422 |
| DOI: | 10.48550/arxiv.1611.00496 |