Dirichlet series for finite combinatorial rank dynamics

Details Dirichlet series for finite combinatorial rank dynamics Dirichlet series for finite combinatorial rank dynamics

2007-05-08

arxiv.org/abs/0705.1067v2

Mathematics

Dynamical Systems

reference for Agmon's theorem added

Scientific paper

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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