Dynamical Zeta Functions for Typical Extensions of Full Shifts

T Ward

doi:10.1006/ffta.1999.0250

Dynamical Zeta Functions for Typical Extensions of Full Shifts

T Ward

School of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Pages (from-to)	232-239
Number of pages	8
Journal	Finite Fields and Their Applications
Volume	5
Issue number	3
DOIs	https://doi.org/10.1006/ffta.1999.0250
Publication status	Published - 1999

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10.1006/ffta.1999.0250Licence: Other

Cite this

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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.",

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AB - 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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DO - 10.1006/ffta.1999.0250

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JO - Finite Fields and Their Applications

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ER -