Self-affine sets with fibered tangents

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 poi...

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Bibliographic Details
Published in:arXiv.org 2015-10
Main Authors: Kaenmaki, Antti, Koivusalo, Henna, Rossi, Eino
Format: Article
Language:English
Subjects:
Tangents
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1505.00958