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), 29572964
MSC (2000):
Primary 37H15, 37B05; Secondary 54H20
Published electronically:
May 13, 2005
MathSciNet review:
2159774
Fulltext PDF Free Access
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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:
http://dx.doi.org/10.1090/S0002993905077774
PII:
S 00029939(05)077774
Received by editor(s):
October 20, 2003
Published electronically:
May 13, 2005
Communicated by:
Michael Handel
Article copyright:
© Copyright 2005
American Mathematical Society
