Orbit closures of generic unipotent flows on homogeneous spaces of \(SL(3,{\mathbb{R}})\)

DOI10.1007/BF01453567zbMath0679.22007OpenAlexW1975863337MaRDI QIDQ1822642

Gregory A. Margulis, Shrikrishna G. Dani

Publication date: 1990

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164629

zbMATH Keywords

latticequadratic formsdiophantine approximationclosed subgroupone-parameter subgroupunipotent matricesfinite F-invariant measure

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Analysis on real and complex Lie groups (22E30) Measures on groups and semigroups, etc. (43A05) Discrete subgroups of Lie groups (22E40) Quadratic forms over global rings and fields (11E12)

Related Items

On the density of S-adic integers near some projective G-varieties, On an Oppenheim-type conjecture for systems of quadratic forms, Limit distributions of polynomial trajectories on homogeneous spaces, From rational billiards to dynamics on moduli spaces, Actions of Cartan subgroups, Oppenheim conjecture for pairs consisting of a linear form and a quadratic form, Invariant and stationary measures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space, Values of pairs involving one quadratic form and one linear form at \(S\)-integral points, Limit distributions of expanding translates of certain orbits on homogeneous spaces, On the space of ergodic invariant measures of unipotent flows, Locally unipotent invariant measures and limit distribution of a sequence of polynomial trajectories on homogeneous spaces, Polynomial effective equidistribution, Finitary analysis in homogeneous spaces, On the space of ergodic invariant measures of unipotent flows, Polynomial effective density in quotients of \(\mathbb{H}^3\) and \(\mathbb{H}^2 \times \mathbb{H}^2\), Uniformly distributed orbits of certain flows on homogeneous spaces, Values of indefinite quadratic forms at integral points and flows on spaces of lattices, Effective estimates on indefinite ternary forms, On the density at integer points of a system comprising an inhomogeneous quadratic form and a linear form, Isolation, equidistribution, and orbit closures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space, Systems of quadratic Diophantine inequalities and the value distribution of quadratic forms, A generic effective Oppenheim theorem for systems of forms, Geometric results on linear actions of reductive Lie groups for applications to homogeneous dynamics, Distribution rigidity for unipotent actions on homogeneous spaces, Density of values of linear maps on quadratic surfaces, Strict measure rigidity for unipotent subgroups of solvable groups, Effective equidistribution for closed orbits of semisimple groups on homogeneous spaces, A UNIPOTENT GROUP ACTION ON A FLAG MANIFOLD AND "GAP SEQUENCES" OF PERMUTATIONS, Parabolic perturbations of unipotent flows on compact quotients of \(\mathrm{SL}(3,\mathbb{R})\), On measures invariant under tori on quotients of semisimple groups, Asymptotic behaviour of trajectories of unipotent flows on homogeneous spaces, Raghunathan's topological conjecture and distributions of unipotent flows, Invariant measures for actions of unipotent groups over local fields on homogeneous spaces, Invariant measures and orbit closures for unipotent actions on homogeneous spaces

Cites Work

• Asymptotic behaviour of trajectories of unipotent flows on homogeneous spaces
• Orbits of horospherical flows
• A simple proof of Borel's density theorem
• Orbits of Euclidean frames under discrete linear groups
• Orbit spaces of unitary representations, ergodic theory, and simple Lie groups
• Asymptotic properties of unitary representations
• Values of quadratic forms at primitive integral points
• Groupes reductifs
• On orbits of unipotent flows on homogeneous spaces
• Divergent trajectories of flows on homogeneous spaces and Diophantine approximation.
• ARITHMETIC PROPERTIES OF DISCRETE SUBGROUPS
• Invariant measures for unipotent translations on homogeneous spaces.
• Ergodic Properties of Affine Transformations and Flows on Nilmanifolds
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item