Dynamical zeta functions for typical extensions of full shifts

Ward, T. (1999) Dynamical zeta functions for typical extensions of full shifts. Finite Fields and Their Applications, 5 (3). pp. 232-239.

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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.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
Depositing User:	Vishal Gautam
Date Deposited:	18 Mar 2011 14:48
Last Modified:	14 Oct 2025 09:32
URI:	https://ueaeprints.uea.ac.uk/id/eprint/19680
DOI:	10.1006/ffta.1999.0250

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