Assouad dimension of planar self-affine sets

Bárány, Balázs; Käenmäki, Antti; Rossi, Eino

doi:10.1090/tran/8224

Assouad dimension of planar self-affine sets
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by Balázs Bárány, Antti Käenmäki and Eino Rossi PDF

Trans. Amer. Math. Soc. 374 (2021), 1297-1326 Request permission

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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