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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

Dirichlet series for finite combinatorial rank dynamics


Authors: G. Everest, R. Miles, S. Stevens and T. Ward
Journal: Trans. Amer. Math. Soc. 362 (2010), 199-227
MSC (2000): Primary 37C30; Secondary 26E30, 12J25
Published electronically: July 30, 2009
MathSciNet review: 2550149
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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.


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Additional Information

G. Everest
Affiliation: School of Mathematics, University of East Anglia, Norwich NR4 7TJ, United Kingdom
Email: g.everest@uea.ac.uk

R. Miles
Affiliation: Department of Mathematics, KTH-Royal Institute of Technology, SE-100 44 Stockholm, Sweden
Email: ricmiles@kth.se

S. Stevens
Affiliation: School of Mathematics, University of East Anglia, Norwich NR4 7TJ, United Kingdom
Email: shaun.stevens@uea.ac.uk

T. Ward
Affiliation: School of Mathematics, University of East Anglia, Norwich NR4 7TJ, United Kingdom
Email: t.ward@uea.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04962-9
Received by editor(s): July 25, 2007
Published electronically: July 30, 2009
Additional Notes: This research was supported by E.P.S.R.C. grant EP/C015754/1.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.