The first cohomology group, mixing and minimal sets of the commutative group of algebraic actions on a torus

DOI10.1007/BF02169057zbMath0984.37004MaRDI QIDQ1125645

A. N. Starkov

Publication date: 12 December 1999

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

zbMATH Keywords

first cohomology groupcohomological rigiditystandard Anosov actions

Mathematics Subject Classification ID

General groups of measure-preserving transformations (28D15) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20)

Related Items (10)

Exponential mixing and smooth classification of commuting expanding maps ⋮ Multi-invariant measures and subsets on nilmanifolds ⋮ Differentiable rigidity for hyperbolic toral actions ⋮ Rigidity properties for some isometric extensions of partially hyperbolic actions on the torus ⋮ On local rigidity of partially hyperbolic affine \(\mathbb{Z}^k\) actions ⋮ Local rigidity of partially hyperbolic actions I. KAM method and \({\mathbb Z^k}\) actions on the torus ⋮ Local rigidity of higher rank non-abelian action on torus ⋮ Global rigidity of higher rank abelian Anosov algebraic actions ⋮ Global rigidity of higher rank Anosov actions on tori and nilmanifolds ⋮ Local rigidity of actions of higher rank abelian groups and KAM method

Cites Work

• Unnamed Item
• First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity
• The cohomology of expansive \(\mathbb{Z}^ d\)-actions by automorphisms of compact, Abelian groups
• Periodic points and invariant pseudomeasures for toral endomorphisms
• Higher cohomology for Abelian groups of toral automorphisms

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