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arXiv · 1505.00958

Self-affine sets with fibered tangents

Antti Kaenmaki·Henna Koivusalo·Eino Rossi
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Abstract

We study tangent sets of strictly self-affine sets in the plane. If a set in this class satisfies the strong separation condition and projects to a line segment for sufficiently many directions, then for each generic point there exists a rotation $\mathcal O$ such that all tangent sets at that point are either of the form $\mathcal O((\mathbb R \times C) \cap B(0,1))$, where $C$ is a closed porous set, or of the form $\mathcal O((\ell \times \{ 0 \}) \cap B(0,1))$, where $\ell$ is an interval.

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Antti Kaenmaki, Henna Koivusalo, Eino Rossi. 2015-05-05. Self-affine sets with fibered tangents. https://doi.org/10.1017/etds.2015.130

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