Dynamical zeta functions for typical extensions of full shifts
Dynamical Systems
2007-05-23 v1 Number Theory
Abstract
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.
Keywords
Cite
@article{arxiv.math/9905175,
title = {Dynamical zeta functions for typical extensions of full shifts},
author = {T. Ward},
journal= {arXiv preprint arXiv:math/9905175},
year = {2007}
}
Comments
6 pages. Finite Fields and Applications, to appear