Hostname: page-component-7dd5485656-dk7s8 Total loading time: 0 Render date: 2025-10-31T14:21:27.004Z Has data issue: false hasContentIssue false
  • English
  • Français

Centralizers of rank-one homeomorphisms

Published online by Cambridge University Press:  03 December 2012

AARON HILL
AARON HILL*
Affiliation:
Mathematics, University of North Texas, Denton, USA (email: aaron.hill@unt.edu)
Get access Rights & Permissions [Opens in a new window]

Abstract

We give a definition for a rank-one homeomorphism of a zero-dimensional Polish space X. We show that if a rank-one homeomorphism of X satisfies a certain non-degeneracy condition, then it has trivial centralizer in the group of all homeomorphisms of X, i.e. it commutes only with its integral powers.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 2 , April 2014 , pp. 543 - 556
Copyright
©2012 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1]Bezuglyi, S., Dooley, A. H. and Kwiatkowski, J.. Topologies on the group of homeomorphisms of a Cantor set. Preprint, 2004, arXiv:math/0410507.Google Scholar
[2]Eremenko, A. and Stepin, A.. Non-unique inclusion in a flow and vast centralizer of a generic measure-preserving transformation. Mat. Sb. 195(12) (2004), 95–108.Google Scholar
[3]Ferenczi, S.. Systems of finite rank. Colloq. Math. 73(1) (1997), 35–65.Google Scholar
[4]Glasner, E. and Weiss, B.. Spatial and non-spatial actions of Polish groups. Ergod. Th. & Dynam. Sys. 25 (2005), 1521–1538.Google Scholar
[5]del Junco, A.. A simple measure-preserving transformation with trivial centralizer. Pacific J. Math. 79(2) (1978), 357–362.Google Scholar
[6]King, J.. The commutant is the weak closure of the powers, for rank-1 transformations. Ergod. Th. & Dynam. Sys. 6 (1986), 363–384.Google Scholar
[7]Melleray, J. and Tsankov, T.. Generic representations of abelian groups and extreme amenability. Israel J. Math. to appear.Google Scholar