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arXiv · 2309.11971

Tangents of invariant sets

Antti Käenmäki·Alex Rutar
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Abstract

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.

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Antti Käenmäki, Alex Rutar. 2023-09-21. Tangents of invariant sets. https://arxiv.org/abs/2309.11971

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