Universally measure-preserving homeomorphisms of Cantor minimal systems

DOI10.1007/s11854-011-0001-3zbMath1233.37003OpenAlexW1989184176MaRDI QIDQ542034

Hisatoshi Yuasa, Toshihiro Hamachi, Michael S. Keane

Publication date: 8 June 2011

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11854-011-0001-3

zbMATH Keywords

symbolic dynamicsCantor minimal systemBratteli diagramedge sequence spacemeasure preserving homeomorphismstopological orbit equivalence

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Symbolic dynamics (37B10) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20) Dynamical systems and the theory of (C^*)-algebras (37A55)

Related Items (5)

Dynamics in dimension zero A survey ⋮ The Morse minimal system is nearly continuously Kakutani equivalent to the binary odometer ⋮ From invariant measures to orbit equivalence, via locally finite groups ⋮ Comparability of clopen sets in a zero-dimensional dynamical system ⋮ Exact number of ergodic invariant measures for Bratteli diagrams

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Orbit equivalence of Cantor minimal systems: a survey and a new proof
• Not finitely but countably Hopf-equivalent clopen sets in a Cantor minimal system
• Connes' bicentralizer problem and uniqueness of the injective factor of type \(III_ 1\)
• A measure theoretical proof of the Connes-Woods theorem on AT-flows
• On hyperfinite factors of type III\(_0\) and Krieger's factors
• On ergodic flows and the isomorphism of factors
• A class of finitary codes
• Bernoulli schemes of the same entropy are finitarily isomorphic
• The relationship between entropy and strong orbit equivalence for the minimal homeomorphisms. II
• Entropy versus orbit equivalence for minimal homeomorphisms
• Strong orbit realization for minimal homeomorphisms
• Full groups of Cantor minimal systems
• Irrational rotation of the circle and the binary odometer are finitarily orbit equivalent
• Dye's theorem in the almost continuous category
• On Groups of Measure Preserving Transformations. I
• The classification of non-singular actions, revisited
• The Relationship Between Entropy and Strong Orbit Equivalence for the Minimal Homeomorphisms (I)
• ORDERED BRATTELI DIAGRAMS, DIMENSION GROUPS AND TOPOLOGICAL DYNAMICS
• WEAK ORBIT EQUIVALENCE OF CANTOR MINIMAL SYSTEMS
• Une classification des facteurs de type ${\rm III}$
• Finitary orbit equivalence and measured Bratteli diagrams
• FINITARY ORBIT EQUIVALENCE OF ODOMETERS
• On non-singular transformations of a measure space. I
• Inductive Limits of Finite Dimensional C ∗ -Algebras

This page was built for publication: Universally measure-preserving homeomorphisms of Cantor minimal systems