Invariant measures and orbit closures for unipotent actions on homogeneous spaces

DOI10.1007/BF01895839zbMath0801.22008OpenAlexW2080729536MaRDI QIDQ1321629

Marina Ratner

Publication date: 21 November 1994

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/58162

zbMATH Keywords

homogeneous spacediscrete subgroupergodic theoryactionconnected Lie groupunipotent subgroup

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Harmonic analysis on homogeneous spaces (43A85) Ergodic theory on groups (22D40) Entropy and other invariants (28D20) Measures on groups and semigroups, etc. (43A05) Discrete subgroups of Lie groups (22E40)

Related Items (24)

Limit distributions of polynomial trajectories on homogeneous spaces ⋮ Raghunathan's conjectures for Cartesian products of real and \(p\)-adic Lie groups ⋮ Eisenstein series on weakly spherical homogeneous spaces of \(GL(n)\) ⋮ Prehomogeneous vector spaces and ergodic theory. I ⋮ On the space of ergodic invariant measures of unipotent flows ⋮ On the space of ergodic invariant measures of unipotent flows ⋮ Unique ergodicity of the horocycle flow on Riemannnian foliations ⋮ Remarks on the dynamics of the horocycle flow for homogeneous foliations by hyperbolic surfaces ⋮ Finiteness of totally geodesic exceptional divisors in Hermitian locally symmetric spaces ⋮ Values of indefinite quadratic forms at integral points and flows on spaces of lattices ⋮ An extension of quantitative nondivergence and applications to Diophantine exponents ⋮ Euler characteristics of Teichmüller curves in genus two ⋮ Prehomogeneous vector spaces and ergodic theory II ⋮ Almost-prime times in horospherical flows on the space of lattices ⋮ Density of values of linear maps on quadratic surfaces ⋮ Prehomogeneous vector spaces and ergodic theory. III ⋮ Finite dimensional representations and subgroup actions on homogeneous spaces ⋮ Minimality and unique ergodicity for subgroup actions ⋮ Measure rigidity for almost linear groups and its applications ⋮ Zimmer's conjecture for actions of \(\mathrm{SL}(m,\mathbb{Z})\) ⋮ Zimmer's conjecture: subexponential growth, measure rigidity, and strong property (T) ⋮ Equidistribution in \(S\)-arithmetic and adelic spaces ⋮ Invariant measures for actions of unipotent groups over local fields on homogeneous spaces ⋮ Unique ergodicity on compact homogeneous spaces

Cites Work

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• Uniform distribution of horocycle orbits for Fuchsian groups
• Raghunathan's topological conjecture and distributions of unipotent flows
• Invariant measures and minimal sets of horospherical flows
• On measure rigidity of unipotent subgroups of semisimple groups
• On Raghunathan's measure conjecture
• Weak mixing and unique ergodicity on homogeneous spaces
• Unique ergodicity of flows on homogeneous spaces
• Raghunathan's conjectures for \(SL(2,{\mathbb{R}{}})\)
• Strict measure rigidity for unipotent subgroups of solvable groups
• Orbit closures of generic unipotent flows on homogeneous spaces of \(SL(3,{\mathbb{R}})\)
• Values of quadratic forms at primitive integral points
• Rigidity of horocycle flows
• Unique Ergodicity of Horospherical Flows
• Measurable Quotients of Unipotent Translations on Homogeneous Spaces
• On the space of ergodic invariant measures of unipotent flows
• On the space of ergodic invariant measures of unipotent flows
• Strict Ergodicity and Transformation of the Torus
• Ergodic Properties of Affine Transformations and Flows on Nilmanifolds
• Rigidity of some translations on homogeneous spaces

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