Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/a-chebotarev-theorem-for-finite-homogeneous-extensions-of-shifts-kVIBWGtrTZ
References (5)
-
W. Parry, M. Pollicott (1986)
The Chebotarov theorem for Galois coverings of Axiom A flowsErgodic Theory and Dynamical Systems, 6
-
J. W. S. Cassels, A. Fröhlich (1967)
Algebraic Number Theory -
J. Cassels, A. Fröhlich (1967)
Algebraic number theory : proceedings of an instructional conference organized by the London Mathematical Society (a Nato Advanced Study Institute) with the support of the International Mathematical Union -
W. Parry, M. Pollicott (1990)
Zeta functions and the periodic orbit structure of hyperbolic dynamics -
W. Ledermann (1973)
Introduction to group theory
- Publisher
- Springer Journals
- Copyright
- Copyright © 1992 by Sociedade Brasileira de Matemática
- Subject
- Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
- ISSN
- 1678-7544
- eISSN
- 1678-7714
- DOI
- 10.1007/BF02584816
- Publisher site
- See Article on Publisher Site
Abstract
We derive a Chebotarev Theorem for finite homogeneous extensions of shifts of finite type. These extensions are of the form $$\tilde \sigma $$ :X×G/H→X×G/H where $$\tilde \sigma $$ (x,gH)=(σx, α(x)gH), for some finite groupG and subgroupH. Given a σ-closed orbit τ, the periods of the $$\tilde \sigma $$ -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.
Journal
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Mar 4, 2007