A ug 2 00 6 Minimal topological actions do not determine the measurable orbit equivalence class
نویسنده
چکیده
We construct a minimal topological action Φ̃ of a non-amenable group on a Cantor set C, which is non-uniquely ergodic and furthermore there exist ergodic invariant measures μ1 and μ2 such that (Φ̃, C, μ1) and (Φ̃, C, μ2) are not orbit equivalent measurable equivalence relations. AMS Subject Classifications: 37A20
منابع مشابه
Minimal topological actions do not determine the measurable orbit equivalence class
We construct an amenable action ˆ of a non-amenable group on a discrete space. This action extends to a minimal topological action ẑ of on a Cantor set C . We show that ẑ is non-uniquely ergodic and furthermore there exist ergodic invariant measures 1 and 2 such that . ẑ ; C; 1/ and . ẑ ; C; 2/ are not orbit equivalent measurable equivalence relations. This also provides an instance of the fail...
متن کاملN ov 2 00 7 Orbit equivalence for Cantor minimal Z 2 - systems
We show that every minimal, free action of the group Z2 on the Cantor set is orbit equivalent to an AF-relation. As a consequence, this extends the classification of minimal systems on the Cantor set up to orbit equivalence to include AF-relations, Z-actions and Z2-actions.
متن کاملA Bratteli Diagram for Commuting Homeomorphisms of the Cantor Set
This paper presents a construction of a sequence of Kakutani-Rohlin Towers and a corresponding simple Bratteli Diagram, B, for a general minimal aperiodic Z d action on a Cantor Set, X, with d 2. This is applied to the description of the orbit structure and to the calculation of the ordered group of coinvariants. For each minimal continuous Z d action on X there is a minimal continuous Z action...
متن کاملv 1 [ m at h . FA ] 1 5 A ug 2 00 0 Representations of Cuntz algebras , loop groups and wavelets Palle
A theorem of Glimm states that representation theory of an NGCR C∗-algebra is always intractable, and the Cuntz algebra ON is a case in point. The equivalence classes of irreducible representations under unitary equivalence cannot be captured with a Borel cross section. Nonetheless, we prove here that wavelet representations correspond to equivalence classes of irreducible representations of ON...
متن کاملFull Groups and Orbit Equivalence in Cantor Dynamics
In this note we consider dynamical systems (X, G) on a Cantor set X satisfying some mild technical conditions. The considered class includes, in particular, minimal and transitive aperiodic systems. We prove that two such systems (X1, G1) and (X2, G2) are orbit equivalent if and only if their full groups are isomorphic as abstract groups. This result is a topological version of the well-known D...
متن کامل