Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Assouad dimension of self-affine carpets with no grid structure   Previous study of the Assouad dimension of planar self-affine sets has relied
heavily on the underlying IFS having a `grid structure', thus allowing for the
use of approximate squares. We study the Assouad dimension of a class of
self-affine carpets which do not have an associated grid structure. We find
that the Assouad dimension is related to the box and Assouad dimensions of the
(self-similar) projection of the self-affine set onto the first coordinate and
to the local dimensions of the projection of a natural Bernoulli measure onto
the first coordinate. In a special case we relate the Assouad dimension of the
Przytycki-Urba\'nski sets to the lower local dimensions of Bernoulli
convolutions.

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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph