Orbits of Euclidean frames under discrete linear groups

DOI10.1007/BF02762053zbMath0457.28008OpenAlexW2032595428MaRDI QIDQ1150719

S. H. Smith

Publication date: 1980

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02762053

zbMATH Keywords

Lie subgroupdiscrete linear groupshorospherical flowsorbits of Euclidean framesp-frame

Mathematics Subject Classification ID

Ergodic theory on groups (22D40) General groups of measure-preserving transformations (28D15) Lie groups (22E99) Set functions and measures on topological groups or semigroups, Haar measures, invariant measures (28C10) Euclidean geometries (general) and generalizations (51M05)

Related Items (19)

Orbits of horospherical flows ⋮ Approximate topological conjugacy ⋮ On \(\text{SL}(n,\mathbb Z)_+\)-orbits on \(\mathbb R^n\) and positive integral solutions of linear inequalities ⋮ On the dynamics of the linear action of SL(n, Z) ⋮ The dynamics of an Action of Sp(2n, Z) ⋮ Limit distributions of expanding translates of certain orbits on homogeneous spaces ⋮ Topological group actions by group automorphisms and Banach representations ⋮ Invariant measures and minimal sets of horospherical flows ⋮ Ergodic theory and the duality principle on homogeneous spaces ⋮ Minimal actions of semisimple groups ⋮ The elementary action on unimodular rows over a monoid ring ⋮ Lie groups ⋮ Dynamics on the space of 2-lattices in 3-space ⋮ Uniform distribution of orbits of lattices on spaces of frames ⋮ Dynamics of horospherical flows ⋮ Orbit closures of generic unipotent flows on homogeneous spaces of \(SL(3,{\mathbb{R}})\) ⋮ On uniformly distributed orbits of certain horocycle flows ⋮ On estimates for integral solutions of linear inequalities ⋮ On lattices acting on boundaries of semi-simple groups

Cites Work

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• On invariant measures, minimal sets and a lemma of Margulis
• Minimality of horospherical flows
• Cartan subgroups and lattices in semi-simple groups
• Flows on Homogeneous Spaces. (AM-53)
• Kolmogorov Automorphisms on Homogeneous Spaces
• Unique Ergodicity of Horospherical Flows
• Ergodicity of Flows on Homogeneous Spaces

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