Assouad dimension of planar self-affine sets

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 s...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2021-02, Vol.374 (2), p.1297-1326
Main Authors: Balázs Bárány, Antti Käenmäki, Eino Rossi
Format: Article
Language:English
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Summary: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.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/8224