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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Uniform periodic point growth in entropy rank one


Authors: Richard Miles and Thomas Ward
Journal: Proc. Amer. Math. Soc. 136 (2008), 359-365
MSC (2000): Primary 22D40, 37A15, 37A35
Published electronically: September 7, 2007
MathSciNet review: 2350424
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Abstract: We show that algebraic dynamical systems with entropy rank one have uniformly exponentially many periodic points in all directions.


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Additional Information

Richard Miles
Affiliation: School of Mathematics, KTH, SE-100 44 Stockholm, Sweden

Thomas Ward
Affiliation: School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, United Kingdom

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09018-1
PII: S 0002-9939(07)09018-1
Received by editor(s): September 25, 2006
Published electronically: September 7, 2007
Additional Notes: This research was supported by E.P.S.R.C. grant EP/C015754/1. Both authors express their thanks to Graham Everest and Shaun Stevens for helpful discussions.
Communicated by: Jane M. Hawkins
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.