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arXiv · 0705.1067

Dirichlet series for finite combinatorial rank dynamics

G. Everest·R. Miles·S. Stevens·T. Ward
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Abstract

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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G. Everest, R. Miles, S. Stevens, T. Ward. 2007-05-08. Dirichlet series for finite combinatorial rank dynamics. https://doi.org/10.1090/s0002-9947-09-04962-9

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