EVEREST, Graham, MILES, Richard, STEVENS, Shaun and WARD, Thomas (2010). Dirichlet series for finite combinatorial rank dynamics. Transactions of the American Mathematical Society (TRAN), 362 (1), 199-227.
Full text not available from this repository.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 to be a rational function of exponential variables. 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.
Item Type: | Article |
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Departments - Does NOT include content added after October 2018: | Faculty of Social Sciences and Humanities > Department of Teacher Education |
Identification Number: | https://doi.org/10.1090/S0002-9947-09-04962-9 |
Page Range: | 199-227 |
Depositing User: | Richard Miles |
Date Deposited: | 26 Jan 2018 14:42 |
Last Modified: | 18 Mar 2021 16:30 |
URI: | https://shura.shu.ac.uk/id/eprint/17229 |
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