Book Review: The ergodic theory of lattice subgroups

DOI10.1090/S0273-0979-2011-01335-0zbMath1321.00024MaRDI QIDQ2949098

Manfred Einsiedler

Publication date: 7 October 2015

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Means on groups, semigroups, etc.; amenable groups (43A07) General groups of measure-preserving transformations and dynamical systems (37A15) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02) External book reviews (00A17) Measure-theoretic ergodic theory (28Dxx)

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Cites Work

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• Mixing of all orders of Lie groups actions
• Asymptotic properties of unitary representations
• Density of integer points on affine homogeneous varieties
• Mixing, counting, and equidistribution in Lie groups
• Unipotent flows and counting lattice points on homogeneous varieties
• The ergodic theorem
• Ergodic theory of amenable group actions. I: The Rohlin lemma
• Pointwise theorems for amenable groups
• Manin’s and Peyre’s conjectures on rational points and adelic mixing

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