Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integer sequences counting periodic points   An existing dialogue between number theory and dynamical systems is advanced.
A combinatorial device gives necessary and sufficient conditions for a sequence
of non-negative integers to count the periodic points in a dynamical system.
This is applied to study linear recurrence sequences which count periodic
points. Instances where the $p$-parts of an integer sequence themselves count
periodic points are studied. The Mersenne sequence provides one example, and
the denominators of the Bernoulli numbers provide another. The methods give a
dynamical interpretation of many classical congruences such as Euler-Fermat for
matrices, and suggest the same for the classical Kummer congruences satisfied
by the Bernoulli numbers.

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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: physics