Conjugations, joinings, and direct products of locally rank one dynamical systems

DOI10.1007/BF02463255zbMath0996.37002OpenAlexW2086717185MaRDI QIDQ1972749

V. V. Ryzhikov, Geoffrey R. Goodson

Publication date: 13 April 2000

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02463255

zbMATH Keywords

ergodic mapCartesian productjoiningsconjugationsfinite rank automorphismfinite rank systemsidentity automorphism

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Dynamical aspects of measure-preserving transformations (37A05)

Related Items (1)

Rank, rigidity of factors, and weak closure of measure-preserving \(\mathbb Z^n\)-actions

Cites Work

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• Systèmes localement de rang un
• Joining-rank and the structure of finite rank mixing transformations
• A canonical structure theorem for finite joining-rank maps
• The isomorphism of measure-preserving transformations with isomorphic Cartesian powers is typical
• Ergodic properties where order 4 implies infinite order
• Connections between the approximative and spectral properties of metric automorphisms
• On the rank of a class of bijective substitutions
• The commutant is the weak closure of the powers, for rank-1 transformations
• MIXING, RANK, AND MINIMAL SELF-JOINING OF ACTIONS WITH AN INVARIANT MEASURE
• Transformations conjugate to their inverses have even essential values
• Ergodic transformations conjugate to their inverses by involutions
• Metric properties of measure preserving homeomorphisms

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