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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.


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.

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Publisher 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
Record Created:12 Oct 2012 12:50
Last Modified:17 Oct 2012 10:37

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