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arXiv · 1611.00496

Genericity of dimension drop on self-affine sets

Antti Käenmäki·Bing Li
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Abstract

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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Antti Käenmäki, Bing Li. 2017-03-03. Genericity of dimension drop on self-affine sets. https://doi.org/10.1016/j.spl.2017.02.028

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