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Dynamical zeta functions for typical extensions of full shifts

Ward, T.

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Authors

T. Ward



Abstract

We consider a family of isometric extensions of the full shift on p symbols (for p a prime) parametrised by a probability space. Using Heath-Brown's work on the Artin conjecture, it is shown that for all but two primes p the set of limit points of the growth rate of periodic points is infinite almost surely. This shows in particular that the dynamical zeta function is not algebraic almost surely.

Citation

Ward, T. (1999). Dynamical zeta functions for typical extensions of full shifts. Finite Fields and Their Applications, 5(3), 232-239. https://doi.org/10.1006/ffta.1999.0250

Journal Article Type Article
Publication Date Jul 1, 1999
Deposit Date Oct 12, 2012
Publicly Available Date Oct 17, 2012
Journal Finite Fields and Their Applications
Print ISSN 1071-5797
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 5
Issue 3
Pages 232-239
DOI https://doi.org/10.1006/ffta.1999.0250

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Accepted Journal Article (129 Kb)
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Copyright Statement
NOTICE: this is the author’s version of a work that was accepted for publication in Finite fields and their applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Finite fields and their applications, 5/3, 1999, 10.1006/ffta.1999.0250





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