Functorial Orbit Counting
Apisit Pakapongpun and Thomas Ward
School of Mathematics
University of East Anglia
We study the functorial and growth properties of closed orbits
for maps. By viewing an arbitrary sequence as the
orbit-counting function for a map, iterates and Cartesian
products of maps define new transformations between integer
sequences. An orbit monoid is associated to any integer
sequence, giving a dynamical interpretation of the Euler
Full version: pdf,
(Concerned with sequences
Received October 28 2008;
revised version received January 20 2009.
Published in Journal of Integer Sequences, February 13 2009.
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