Dynamical zeta functions for typical extensions of full shifts

Details Dynamical zeta functions for typical extensions of full shifts Dynamical zeta functions for typical extensions of full shifts

1999-05-27

arxiv.org/abs/math/9905175v1

Finite Fields and their Applications 5, No.3, 1999, 232-239

Mathematics

Dynamical Systems

6 pages. Finite Fields and Applications, to appear

Scientific paper

10.1006/ffta.1999.0250

We 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.

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