Cookies

We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.


Durham Research Online
You are in:

Dirichlet series for finite combinatorial rank dynamics.

Everest, G. and Miles, R. and Stevens, S. and Ward, T. (2010) 'Dirichlet series for finite combinatorial rank dynamics.', Transactions of the American Mathematical Society., 362 (01). pp. 199-227.

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.

Item Type:Article
Full text:PDF - Accepted Version (489Kb)
Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1090/S0002-9947-09-04962-9
Publisher statement:First published in Transactions of the American Mathematical Society in 2010, volume 362 published by the American Mathematical Society. © Copyright 2010 American Mathematical Society.
Record Created:12 Oct 2012 10:05
Last Modified:14 Dec 2012 13:56

Social bookmarking: del.icio.usConnoteaBibSonomyCiteULikeFacebookTwitterExport: EndNote, Zotero | BibTex
Usage statisticsLook up in GoogleScholar | Find in a UK Library