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Dynamical Zeta Functions for Typical Extensions of Full Shifts

โœ Scribed by T. Ward


Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
107 KB
Volume
5
Category
Article
ISSN
1071-5797

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โœฆ 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.


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