Everest, G. and Miles, R. and Stevens, S. and Ward, T. (2010) 'Dirichlet series for finite combinatorial rank dynamics.', Transactions of the American Mathematical Society., 362 (01). pp. 199-227.
We introduce a class of group endomorphisms -- those of finite combinatorial rank -- exhibiting slow orbit growth. An associated Dirichlet series is used to obtain an exact orbit counting formula, and in the connected case this series is shown to have a closed rational form. Analytic properties of the Dirichlet series are related to orbit-growth asymptotics: depending on the location of the abscissa of convergence and the degree of the pole there, various orbit-growth asymptotics are found, all of which are polynomially bounded.
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|Publisher Web site:||http://dx.doi.org/10.1090/S0002-9947-09-04962-9|
|Publisher statement:||First published in Transactions of the American Mathematical Society in 2010, volume 362 published by the American Mathematical Society. © Copyright 2010 American Mathematical Society.|
|Record Created:||12 Oct 2012 10:05|
|Last Modified:||14 Dec 2012 13:56|
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