Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Iterated functions and the Cantor set in one dimension   In this paper we consider the long-term behavior of points in ${\mathbb R}$
under iterations of continuous functions. We show that, given any Cantor set
$\Lambda^*$ embedded in ${\mathbb R}$, there exists a continuous function
$F^*:{\mathbb R}\to{\mathbb R}$ such that the points that are bounded under
iterations of $F^*$ are just those points in $\Lambda^*$. In the course of
this, we find a striking similarity between the way in which we construct the
Cantor middle-thirds set, and the way in which we find the points bounded under
iterations of certain continuous functions.

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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
33
The categories of this paper are: plasm-ph