Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thresholds for One-Parameter Families of Affine Iterated Function
  Systems   This paper examines thresholds for certain properties of the attractor of a
general one-parameter affine family of iterated functions systems. As the
parameter increases, the iterated function system becomes less contractive, and
the attractor evolves. Thresholds are studied for the following properties: the
existence of an attractor, the connectivity of the attractor, and the existence
of non-empty interior of the attractor. Also discussed are transition phenomena
between existence and non-existence of an attractor.

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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: nlin