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Assouad dimension of planar self-affine sets (1906.11007v2)
Published 26 Jun 2019 in math.DS, math.CA, and math.MG
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.