A Chebotarev Theorem for finite homogeneous extensions of shifts |
| |
Authors: | Mohd Salmi Md Noorani William Parry |
| |
Institution: | (1) Mathematics Institute, University of Warwick, CV4 7AL Coventry, UK |
| |
Abstract: | We derive a Chebotarev Theorem for finite homogeneous extensions of shifts of finite type. These extensions are of the form
:X×G/H→X×G/H where
(x,gH)=(σx, α(x)gH), for some finite groupG and subgroupH. Given a σ-closed orbit τ, the periods of the
-closed orbits covering τ define a partition of the integer |G/H|. The theorem then gives us an asymptotic formula for the number of closed orbits with respect to the various partitions
of the integer |G/H|. We apply our theorem to the case of a finite extension and of an automorphism extension of shifts of finite type. We also
give a further application to ‘automorphism extensions’ of hyperbolic toral automorphisms.
Financially supported by Universiti Kebangsaan Malaysia |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|