### 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 language | English |
---|---|

Pages (from-to) | 137-151 |

Number of pages | 15 |

Journal | Boletim da Sociedade Brasileira de Matemática |

Volume | 23 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Mar 1992 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Boletim da Sociedade Brasileira de Matemática*,

*23*(1-2), 137-151. https://doi.org/10.1007/BF02584816

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

Research output: Contribution to journal › Article

*Boletim da Sociedade Brasileira de Matemática*, vol. 23, no. 1-2, pp. 137-151. https://doi.org/10.1007/BF02584816

}

TY - JOUR

T1 - A Chebotarev Theorem for finite homogeneous extensions of shifts

AU - Md. Noorani, Mohd. Salmi

AU - Parry, William

PY - 1992/3

Y1 - 1992/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=51249162894&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51249162894&partnerID=8YFLogxK

U2 - 10.1007/BF02584816

DO - 10.1007/BF02584816

M3 - Article

AN - SCOPUS:51249162894

VL - 23

SP - 137

EP - 151

JO - Bulletin of the Brazilian Mathematical Society

JF - Bulletin of the Brazilian Mathematical Society

SN - 1678-7544

IS - 1-2

ER -