Invariant sets and measures of nonexpansive group automorphisms

DOI10.1007/BF02984405zbMath1076.28014arXivmath/0303121OpenAlexW2063309700MaRDI QIDQ1769168

Klaus Schmidt, Elon Lindenstrauss

Publication date: 21 March 2005

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0303121

zbMATH Keywords

nonexpansive group automorphismsRuldoph's theorem

Mathematics Subject Classification ID

Related Items (13)

Representations of toral automorphisms ⋮ Dynamical directions in numeration ⋮ Density of metric entropies for linear toral automorphisms ⋮ The almost Borel structure of surface diffeomorphisms, Markov shifts and their factors ⋮ Intrinsic ergodicity via obstruction entropies ⋮ Disintegrations of non‐hyperbolic ergodic measures along the center foliation of DA maps ⋮ Equilibrium states for partially hyperbolic diffeomorphisms with hyperbolic linear part ⋮ Equilibrium measures for certain isometric extensions of Anosov systems ⋮ On the Bernoulli property for certain partially hyperbolic diffeomorphisms ⋮ Ergodic universality of some topological dynamical systems ⋮ Limiting distributions of curves under geodesic flow on hyperbolic manifolds ⋮ Rigidity of multiparameter actions ⋮ Symbolic representations of nonexpansive group automorphisms

Cites Work

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• Flows on homogeneous spaces and Diophantine approximation on manifolds
• Normal numbers, entropy, translations
• Ergodic automorphisms of \(T^ n\) are Bernoulli shifts
• ×2 and ×3 invariant measures and entropy
• Automorphisms of Compact Abelian Groups and Affine Varieties
• Some results of uniform distribution in the multidimensional torus
• Invariant measures for higher-rank hyperbolic abelian actions
• Dynamical systems of algebraic origin

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