On orbits of unipotent flows on homogeneous spaces

DOI10.1017/S0143385700002248zbMath0557.22008OpenAlexW2169687370MaRDI QIDQ3222385

Shrikrishna G. Dani

Publication date: 1984

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385700002248

zbMATH Keywords

latticeunipotent one-parameter subgroupergodic invariant measure

Mathematics Subject Classification ID

Homogeneous spaces (22F30) Discrete subgroups of Lie groups (22E40) Topological transformation groups (57S99) Homogeneous flows (37A17)

Related Items (28)

Invariant and stationary measures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space ⋮ Limit distributions of expanding translates of certain orbits on homogeneous spaces ⋮ Equidistribution of expanding translates of curves and Diophantine approximation on matrices ⋮ Escape of mass and entropy for diagonal flows in real rank one situations ⋮ Equidistribution of curves in homogeneous spaces and Dirichlet's approximation theorem for matrices ⋮ Polynomial effective equidistribution ⋮ Finitary analysis in homogeneous spaces ⋮ Effective equidistribution for multiplicative Diophantine approximation on lines ⋮ Uniformly distributed orbits of certain flows on homogeneous spaces ⋮ Non-divergence of unipotent flows on quotients of rank-one semisimple groups ⋮ An extension of quantitative nondivergence and applications to Diophantine exponents ⋮ Expanding curves in \(\mathrm T^{1}(\mathbb H^{n})\) under geodesic flow and equidistribution in homogeneous spaces ⋮ A shrinking target problem with target at infinity in rank one homogeneous spaces ⋮ Shadow Lemma and nondivergence of the horospheres of a geometrically finite manifold. ⋮ Geometric results on linear actions of reductive Lie groups for applications to homogeneous dynamics ⋮ Almost-prime times in horospherical flows on the space of lattices ⋮ Hausdorff dimension of divergent trajectories on homogeneous spaces ⋮ Equidistribution of expanding curves in homogeneous spaces and Diophantine approximation on square matrices ⋮ Limiting distributions of curves under geodesic flow on hyperbolic manifolds ⋮ Asymptotic evolution of smooth curves under geodesic flow on hyperbolic manifolds ⋮ Orbit closures of generic unipotent flows on homogeneous spaces of \(SL(3,{\mathbb{R}})\) ⋮ Values of quadratic forms at primitive integral points ⋮ (Non)-escape of mass and equidistribution for horospherical actions on trees ⋮ Badly approximable points on manifolds and unipotent orbits in homogeneous spaces ⋮ Equidistribution of expanding translates of curves in homogeneous spaces with the action of \((\mathrm{SO}(n, 1))^k\) ⋮ Unnamed Item ⋮ Compactness of minimal closed invariant sets of actions of unipotent groups ⋮ Invariant measures for actions of unipotent groups over local fields on homogeneous spaces

Cites Work

• Unnamed Item
• On invariant measures, minimal sets and a lemma of Margulis
• Uniform distribution of horocycle orbits for Fuchsian groups
• Invariant measures and minimal sets of horospherical flows
• Invariant measures of horospherical flows on non-compact homogeneous spaces
• Fundamental domains for lattices in (R-)rank 1 semisimple Lie groups

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