Invariant measures and minimal sets of horospherical flows

DOI10.1007/BF01389173zbMath0498.58013OpenAlexW2043289687WikidataQ106127380 ScholiaQ106127380MaRDI QIDQ1171318

Shrikrishna G. Dani

Publication date: 1981

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142826

zbMATH Keywords

reductive Lie grouparithmetic latticesergodicity of horocycle flowsmaximal horospherical subgroupunique ergodicity of flows

Mathematics Subject Classification ID

Ergodic theory on groups (22D40) Semisimple Lie groups and their representations (22E46) Discrete subgroups of Lie groups (22E40) Geodesic flows in symplectic geometry and contact geometry (53D25) Ergodic theory (37A99) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) One-parameter continuous families of measure-preserving transformations (28D10)

Related Items (40)

Orbits of horospherical flows ⋮ Sparse equidistribution of unipotent orbits in finite-volume quotients of \(\mathrm{PSL}(2,\mathbb R)\) ⋮ Invariant and stationary measures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space ⋮ Eisenstein series and equidistribution of Lebesgue probability measures on compact leaves of the horocycle foliations of Bianchi 3-orbifolds ⋮ Prehomogeneous vector spaces and ergodic theory. I ⋮ On orbits of unipotent flows on homogeneous spaces ⋮ Finitary analysis in homogeneous spaces ⋮ Horospherical invariant measures and a rank dichotomy for Anosov groups ⋮ On the density of some sparse horocycles ⋮ Effective equidistribution for multiplicative Diophantine approximation on lines ⋮ Values of indefinite quadratic forms at integral points and flows on spaces of lattices ⋮ On the uniform equidistribution of long closed horocycles ⋮ On measure rigidity of unipotent subgroups of semisimple groups ⋮ Isolation, equidistribution, and orbit closures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space ⋮ Apollonian circle packings and closed horospheres on hyperbolic 3-manifolds ⋮ Equidistribution of families of expanding horospheres on moduli spaces of hyperbolic surfaces ⋮ Rigidity of some translations on homogeneous spaces ⋮ Prehomogeneous vector spaces and ergodic theory II ⋮ Slow chaos in surface flows ⋮ Almost-prime times in horospherical flows on the space of lattices ⋮ Distribution rigidity for unipotent actions on homogeneous spaces ⋮ Effective equidistribution of twisted horocycle flows and horocycle maps ⋮ Raghunathan's conjectures for \(SL(2,{\mathbb{R}{}})\) ⋮ Prehomogeneous vector spaces and ergodic theory. III ⋮ Strict measure rigidity for unipotent subgroups of solvable groups ⋮ Limiting distributions of translates of divergent diagonal orbits ⋮ Dynamics of horospherical flows ⋮ Values of quadratic forms at primitive integral points ⋮ (Non)-escape of mass and equidistribution for horospherical actions on trees ⋮ Parabolic perturbations of unipotent flows on compact quotients of \(\mathrm{SL}(3,\mathbb{R})\) ⋮ On uniformly distributed orbits of certain horocycle flows ⋮ On ergodic averages for affine lattice actions on tori ⋮ Uniform distribution of horocycle orbits for Fuchsian groups ⋮ Commutator methods for the spectral analysis of uniquely ergodic dynamical systems ⋮ Distribution of cusp sections in the Hilbert modular orbifold ⋮ Gaps of saddle connection directions for some branched covers of tori ⋮ 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

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