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arXiv · 1906.11007

Assouad dimension of planar self-affine sets

Balázs Bárány·Antti Käenmäki·Eino Rossi
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Abstract

We calculate the Assouad dimension of a planar self-affine set $X$ satisfying the strong separation condition and the projection condition and show that $X$ is minimal for the conformal Assouad dimension. Furthermore, we see that such a self-affine set $X$ adheres to very strong tangential regularity by showing that any two points of $X$, which are generic with respect to a self-affine measure having simple Lyapunov spectrum, share the same collection of tangent sets.

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Balázs Bárány, Antti Käenmäki, Eino Rossi. 2019-06-26. Assouad dimension of planar self-affine sets. https://arxiv.org/abs/1906.11007

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