Dirichlet series for finite combinatorial rank dynamics

G Everest, R Miles, S Stevens, T Ward

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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.
Original languageEnglish
Pages (from-to)199-227
Number of pages29
JournalTransactions of the American Mathematical Society
Issue number1
Publication statusPublished - 2010

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