Orientation of piecewise powers of a minimal homeomorphism

Title: Orientation of piecewise powers of a minimal homeomorphism
Creator: Reid, Colin D.
Relation: ARC.FL170100032 http://purl.org/au-research/grants/arc/FL170100032
Relation: Journal of the Australian Mathematical Society Vol. 113, Issue 2, p. 226-256
Publisher Link: http://dx.doi.org/10.1017/S1446788721000197
Publisher: Cambridge University Press
Resource Type: journal article
Date: 2022
Description: 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].
Subject: Cantor minimal systems; topological full group; homeomorphism; topological dynamics
Identifier: http://hdl.handle.net/1959.13/1451981
Identifier: uon:44329
Identifier: ISSN:1446-7887
Language: eng
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