Dynamical zeta functions for typical extensions of full shifts

T. Ward

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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 languageEnglish
Pages (from-to)232-239
Number of pages8
JournalFinite Fields and Their Applications
Issue number3
Publication statusPublished - 1999

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