Invariant measures on G/Γ for split simple Lie groups G

DOI10.1002/cpa.10092zbMath1022.22023OpenAlexW1905444936MaRDI QIDQ4425996

Manfred Einsiedler, Anatole Katok

Publication date: 15 September 2003

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/cpa.10092

zbMATH Keywords

latticeinvariant measuresrigidityhyperbolic actionshigher-rank abelian groupssimple split connected Lie group

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Measurable group actions (22F10)

Related Items (20)

Joinings of higher-rank diagonalizable actions on locally homogeneous spaces ⋮ On the work of Rodriguez Hertz on rigidity in dynamics ⋮ Multi-invariant measures and subsets on nilmanifolds ⋮ A Haar component for quantum limits on locally symmetric spaces ⋮ Diagonal actions in positive characteristic ⋮ Joinings of higher rank torus actions on homogeneous spaces ⋮ Smooth ergodic theory of \(\mathbb{Z}^d \)-actions ⋮ Symmetry of entropy in higher rank diagonalizable actions and measure classification ⋮ Anatole Katok ⋮ Entropy bounds and quantum unique ergodicity for Hecke eigenfunctions on division algebras ⋮ Non-uniform measure rigidity for ℤ^{𝕜} actions of symplectic type ⋮ Rigidity properties of ℤ^{𝕕}-actions on tori and solenoids ⋮ Spectra of hyperbolic surfaces ⋮ Distribution of periodic torus orbits on homogeneous spaces ⋮ The work of Einsiedler, Katok and Lindenstrauss on the Littlewood conjecture ⋮ Invariant measures and measurable projective factors for actions of higher-rank lattices on manifolds ⋮ On measures invariant under tori on quotients of semisimple groups ⋮ Rigidity properties for commuting automorphisms on tori and solenoids ⋮ Rigidity of multiparameter actions ⋮ Rigidity of measures -- the high entropy case and non-commuting foliations

Cites Work

• Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation
• Strong Rigidity of Locally Symmetric Spaces. (AM-78)
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