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Orientation Of Piecewise Powers Of A Minimal Homeomorphism

We show that, given a compact minimal system (X,g) and an element h of the topological full group τ[g] of g, the infinite orbits of h admit a locally constant orientation with respect to the orbits of g. We use this to obtain a clopen partition of (X,G) into minimal and periodic parts, where G is any virtually polycyclic subgroup of τ[g] . We also use the orientation of orbits to give a refinement of the index map and to describe the role in τ[g] of the submonoid generated by the induced transformations of g. Finally, we consider the problem, given a homeomorphism h of the Cantor space X, of determining whether or not there exists a minimal homeomorphism g of X such that h∈τ[g] .

Ketersediaan

Informasi Detail

Judul Seri

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY; Vol.113 Issue 2 October 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 226-256

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

CANTOR MINIMAL SYSTEMS
TOPOLOGICAL FULL GROUP

Info Detail Spesifik

https://doi.org/10.1017/S1446788721000197

Pernyataan Tanggungjawab

Colin D. Reid

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