The Rokhlin lemma for homeomorphisms of a Cantor set

Authors:
S. Bezuglyi, A. H. Dooley and K. Medynets

Journal:
Proc. Amer. Math. Soc. **133** (2005), 2957-2964

MSC (2000):
Primary 37H15, 37B05; Secondary 54H20

DOI:
https://doi.org/10.1090/S0002-9939-05-07777-4

Published electronically:
May 13, 2005

MathSciNet review:
2159774

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Abstract | References | Similar Articles | Additional Information

Abstract: For a Cantor set , let denote the group of all homeomorphisms of . The main result of this note is the following theorem. Let be an aperiodic homeomorphism, let be Borel probability measures on , and let and . Then there exists a clopen set such that the sets are disjoint and . Several corollaries of this result are given. In particular, it is proved that for any aperiodic the set of all homeomorphisms conjugate to is dense in the set of aperiodic homeomorphisms.

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Additional Information

**S. Bezuglyi**

Affiliation:
Institute for Low Temperature Physics, National Academy of Sciences of Ukraine, Kharkov, Ukraine

Email:
bezuglyi@ilt.kharkov.ua

**A. H. Dooley**

Affiliation:
School of Mathematics, University of New South Wales, Sydney, Australia

Email:
a.dooley@unsw.edu.au

**K. Medynets**

Affiliation:
Institute for Low Temperature Physics, National Academy of Sciences of Ukraine, Kharkov, Ukraine

Email:
medynets@ilt.kharkov.ua

DOI:
https://doi.org/10.1090/S0002-9939-05-07777-4

Received by editor(s):
October 20, 2003

Published electronically:
May 13, 2005

Communicated by:
Michael Handel

Article copyright:
© Copyright 2005
American Mathematical Society