Dynamical zeta functions for typical extensions of full shifts

Ward, T.

doi:10.1006/ffta.1999.0250

Dynamical zeta functions for typical extensions of full shifts

Ward, T.

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
Electronic ISSN	1090-2465
Publisher	Elsevier
Peer Reviewed	Peer Reviewed
Volume	5
Issue	3
Pages	232-239
DOI	https://doi.org/10.1006/ffta.1999.0250
Public URL	https://durham-repository.worktribe.com/output/1502456

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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