Raghunathan's topological conjecture and distributions of unipotent flows
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Publication:810158
DOI10.1215/S0012-7094-91-06311-8zbMath0733.22007WikidataQ105982913 ScholiaQ105982913MaRDI QIDQ810158
Publication date: 1991
Published in: Duke Mathematical Journal (Search for Journal in Brave)
latticeorbithomogeneous spaceconnected real Lie groupone-parameter subgroupconnected Lie groupunipotent subgroupAd-unipotent subgroupdistribution rigidityRaghunathan's topological conjecturetopologically rigidunipotent actionunipotent linear map
Ergodic theory on groups (22D40) Dynamics induced by flows and semiflows (37C10) Discrete subgroups of Lie groups (22E40)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Horocycle flows, joinings and rigidity of products
- Uniform distribution of horocycle orbits for Fuchsian groups
- Uniformly distributed orbits of certain flows on homogeneous spaces
- Entropy and isomorphism theorems for actions of amenable groups
- The Mautner phenomenon for general unitary representations
- Invariant measures and minimal sets of horospherical flows
- On measure rigidity of unipotent subgroups of semisimple groups
- On Raghunathan's measure conjecture
- 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
- Group structure and the pointwise ergodic theorem for connected amenable groups
- Fuchsian groups and transitive horocycles
- Distribution rigidity for unipotent actions on homogeneous spaces
- Zero-Entropy Affine Maps on Homogeneous Spaces
- Flows on Homogeneous Spaces: A New Look
- Strict Ergodicity and Transformation of the Torus
- Ergodic Properties of Affine Transformations and Flows on Nilmanifolds
- Groups of Automorphisms of Borel Spaces
- Rigidity of some translations on homogeneous spaces