Dirichlet series for finite combinatorial rank dynamics

Everest, G.; Miles, R.; Stevens, S.; Ward, T.

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.

Citation

Everest, G., Miles, R., Stevens, S., & Ward, T. (2010). Dirichlet series for finite combinatorial rank dynamics. Transactions of the American Mathematical Society, 362(01), 199-227. https://doi.org/10.1090/s0002-9947-09-04962-9

• Journal Article Type: Article
• Publication Date: Jan 1, 2010
• Deposit Date: Oct 12, 2012
• Publicly Available Date: Dec 14, 2012
• Journal: Transactions of the American Mathematical Society
• Print ISSN: 0002-9947
• Electronic ISSN: 1088-6850
• Publisher: American Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 362
• Issue: 01
• Pages: 199-227
• DOI: https://doi.org/10.1090/s0002-9947-09-04962-9
• Public URL: https://durham-repository.worktribe.com/output/1495421