Dirichlet series for finite combinatorial rank dynamics
2009; American Mathematical Society; Volume: 362; Issue: 01 Linguagem: Inglês
10.1090/s0002-9947-09-04962-9
ISSN1088-6850
AutoresGraham Everest, Richard Miles, Shaun Stevens, Thomas Ward,
Tópico(s)Stochastic processes and statistical mechanics
ResumoWe 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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