A nonhomogeneous orbit closure of a diagonal subgroup

DOI10.4007/annals.2010.171.557zbMath1192.22006OpenAlexW2085271248MaRDI QIDQ974049

François Maucourant

Publication date: 27 May 2010

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: http://annals.princeton.edu/annals/2010/171-1/p14.xhtml

zbMATH Keywords

topological rigiditydiagonal subgroups actionsNonhomogeneous orbits

Mathematics Subject Classification ID

Topological dynamics (37B99) Discrete subgroups of Lie groups (22E40)

Related Items (8)

Homogeneous orbit closures and applications ⋮ Multi-invariant measures and subsets on nilmanifolds ⋮ On topologically big divergent trajectories ⋮ Topological self-joinings of Cartan actions by toral automorphisms ⋮ A solution to a problem of Cassels and Diophantine properties of cubic numbers ⋮ Chabauty compactification of the space of Cartan subgroups of \(\mathrm{SL}_n(\mathbb R)\) ⋮ Closures of locally divergent orbits of maximal tori and values of homogeneous forms ⋮ Times two, three, five orbits on \(\mathbb{T}^2\)

Cites Work

• Raghunathan's topological conjecture and distributions of unipotent flows
• Invariant measures and the set of exceptions to Littlewood's conjecture
• Uniformly distributed orbits of certain flows on homogeneous spaces
• Cartan subgroups and lattices in semi-simple groups
• Rigidity of weakly hyperbolic actions of higher real rank semisimple Lie groups and their lattices
• On sets invariant under the action of the diagonal group
• Bi-invariant sets and measures have integer Hausdorff dimension
• Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation
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