2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98504We consider a family of isometric extensions of the full shift on p symbols (for p a prime) parametrized 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.6 pages. Finite Fields and Applications, to appearDynamical SystemsNumber Theory22D40, 58F20text