Journal article
The Rokhlin lemma for homeomorphisms of a Cantor set
Proceedings of the American Mathematical Society, Vol.133(10), pp.2957-2964
2005
DOI: 10.1090/S0002-9939-05-07777-4
Abstract
For a Cantor set X, let Homeo(X) denote the group of all homeomorphisms of X. The main result of this note is the following theorem. Let T ∈ Homeo(X) be an aperiodic homeomorphism, let μ1,μ2,.,μkbe Borel probability measures on X, and let e > 0 and n > 2. Then there exists a clopen set E C X such that the sets E,TE,Tn-1E are disjoint and μi(E ∪ TE ∪. ∪ Tn-1E) > 1-ε, i = 1,., k. Several corollaries of this result are given. In particular, it is proved that for any aperiodic T ∈ Homeo(X) the set of all homeomorphisms conjugate to T is dense in the set of aperiodic homeomorphisins.
Details
- Title: Subtitle
- The Rokhlin lemma for homeomorphisms of a Cantor set
- Creators
- S BezuglyiK MedynetsA. H Dooley
- Resource Type
- Journal article
- Publication Details
- Proceedings of the American Mathematical Society, Vol.133(10), pp.2957-2964
- DOI
- 10.1090/S0002-9939-05-07777-4
- ISSN
- 0002-9939
- eISSN
- 1088-6826
- Language
- English
- Date published
- 2005
- Academic Unit
- Mathematics
- Record Identifier
- 9983985940802771
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