Dirichlet series for finite combinatorial rank dynamics
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- by G. Everest, R. Miles, S. Stevens and T. Ward PDF
- Trans. Amer. Math. Soc. 362 (2010), 199-227 Request permission
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.References
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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
- MR Author ID: 678092
- Email: shaun.stevens@uea.ac.uk
- T. Ward
- Affiliation: School of Mathematics, University of East Anglia, Norwich NR4 7TJ, United Kingdom
- MR Author ID: 180610
- Email: t.ward@uea.ac.uk
- 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.
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 199-227
- MSC (2000): Primary 37C30; Secondary 26E30, 12J25
- DOI: https://doi.org/10.1090/S0002-9947-09-04962-9
- MathSciNet review: 2550149