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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)
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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.

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

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