A Chebotarev Theorem for finite homogeneous extensions of shifts

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We derive a Chebotarev Theorem for finite homogeneous extensions of shifts of finite type. These extensions are of the form {Mathematical expression}:X×G/H→X×G/H where {Mathematical expression}(x, gH)=(σx, α(x)gH), for some finite group G and subgroup H. Given a σ-closed orbit τ, the periods of the {Mathematical expression}-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.

Original languageEnglish
Pages (from-to)137-151
Number of pages15
JournalBoletim da Sociedade Brasileira de Matemática
Volume23
Issue number1-2
DOIs
Publication statusPublished - Mar 1992
Externally publishedYes

Fingerprint

Closed Orbit
Shift of Finite Type
Theorem
Automorphism
Partition
Integer
Asymptotic Formula
Automorphisms
Finite Group
Covering
Subgroup

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

A Chebotarev Theorem for finite homogeneous extensions of shifts. / Md. Noorani, Mohd. Salmi; Parry, William.

In: Boletim da Sociedade Brasileira de Matemática, Vol. 23, No. 1-2, 03.1992, p. 137-151.

Research output: Contribution to journalArticle

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