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COCYCLES FOR CANTOR MINIMAL ℤd-SYSTEMS.
- Source :
-
International Journal of Mathematics . Sep2009, Vol. 20 Issue 9, p1107-1135. 29p. 1 Diagram. - Publication Year :
- 2009
-
Abstract
- We consider a minimal, free action, φ, of the group ℤd on the Cantor set X, for d ≥ 1. We introduce the notion of small positive cocycles for such an action. We show that the existence of such cocycles allows the construction of finite Kakutani–Rohlin approximations to the action. In the case, d = 1, small positive cocycles always exist and the approximations provide the basis for the Bratteli–Vershik model for a minimal homeomorphism of X. Finally, we consider two classes of examples when d = 2 and show that such cocycles exist in both. [ABSTRACT FROM AUTHOR]
- Subjects :
- *COCYCLES
*DYNAMICS
*HOMEOMORPHISMS
*HYPOTHESIS
*HOMOLOGY theory
Subjects
Details
- Language :
- English
- ISSN :
- 0129167X
- Volume :
- 20
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- International Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 44694878
- Full Text :
- https://doi.org/10.1142/S0129167X09005686