Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complexity of injective piecewise contracting interval maps   We study the complexity of the itineraries of injective piecewise contracting
maps on the interval. We prove that for any such map the complexity function of
any itinerary is eventually affine. We also prove that the growth rate of the
complexity is bounded from above by the number $N-1$ of discontinuities of the
map. To show that this bound is optimal, we construct piecewise affine
contracting maps whose itineraries all have the complexity $(N-1)n +1$. In
these examples, the asymptotic dynamics takes place in a minimal Cantor set
containing all the discontinuities.

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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
3
The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol