Orbit equivalence for Cantor minimal Z²-systems

2006/09/24 by Thierry Giordano, Hiroki Matui, Giordano, Thierry +5 · 3 citations
Mathematics · #37B05 #Advanced Operator Algebra Research #Dynamical Systems (math.DS) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.math/0609668

openalex publication_date 2006/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• ℤ²-dimension groups
• Stabilized automorphism groups and full groups of odometers
• Dynamical Systems with Bounded Condition and C^*-algebras

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