Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A strongly irreducible affine iterated function system with two
  invariant measures of maximal dimension   A classical theorem of Hutchinson asserts that if an iterated function system
acts on $\mathbb{R}^d$ by similitudes and satisfies the open set condition then
it admits a unique self-similar measure with Hausdorff dimension equal to the
dimension of the attractor. In the class of measures on the attractor which
arise as the projections of shift-invariant measures on the coding space, this
self-similar measure is the unique measure of maximal dimension. In the context
of affine iterated function systems it is known that there may be multiple
shift-invariant measures of maximal dimension if the linear parts of the
affinities share a common invariant subspace, or more generally if they
preserve a finite union of proper subspaces of $\mathbb{R}^d$. In this note we
construct examples where multiple invariant measures of maximal dimension exist
even though the linear parts of the affinities do not preserve a finite union
of proper subspaces.

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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph