Dynamical Zeta Functions for Typical Extensions of Full Shifts

✍ Scribed by T. Ward

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 107 KB
• Volume: 5
• Category: Article
• ISSN: 1071-5797
• DOI: 10.1006/ffta.1999.0250

✦ Synopsis

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 in"nite almost surely. This shows in particular that the dynamical zeta function is not algebraic almost surely.