Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast approximation of the affinity dimension for dominated affine
  iterated function systems   In 1988 K. Falconer introduced a formula which predicts the value of the
Hausdorff dimension of the attractor of an affine iterated function system. The
value given by this formula -- sometimes referred to as the affinity dimension
-- is known to agree with the Hausdorff dimension both generically and in an
increasing range of explicit cases. It is however a nontrivial problem to
estimate the numerical value of the affinity dimension for specific iterated
function systems. In this article we substantially extend an earlier result of
M. Pollicott and P. Vytnova on the computation of the affinity dimension.
Pollicott and Vytnova's work applies to planar invertible affine contractions
with positive linear parts under several additional conditions which among
other things constrain the affinity dimension to be between 0 and 1. We extend
this result by passing from planar self-affine sets to self-affine sets in
arbitrary dimensions, relaxing the positivity hypothesis to a domination
condition, and removing all other constraints including that on the range of
values of the affinity dimension. We provide some explicit examples of two- and
three-dimensional affine iterated function systems for which the affinity
dimension can be calculated to more than 30 decimal places.

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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc