Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial Entropy and Expansivity   In this paper we study the polynomial entropy of homeomorphism on compact
metric space. We construct a homeomorphism on a compact metric space with
vanishing polynomial entropy that it is not equicontinuous. Also we give
examples with arbitrarily small polynomial entropy. Finally, we show that
expansive homeomorphisms and positively expansive maps of compact metric spaces
with infinitely many points have polynomial entropy greater or equal than 1.

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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
18
The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: physics