Dynamical Zeta Functions for Typical Extensions of Full Shifts
نویسنده
چکیده
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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ar X iv : m at h / 99 05 17 5 v 1 [ m at h . D S ] 2 7 M ay 1 99 9 DYNAMICAL ZETA FUNCTIONS FOR TYPICAL EXTENSIONS OF FULL SHIFTS
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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تاریخ انتشار 1999