Bounded orbits of nonquasiunipotent flows on homogeneous spaces | Zendy

Dmitry Kleinbock | Zendy; Gregori Aleksandrovitch Margulis | Zendy

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Bounded orbits of nonquasiunipotent flows on homogeneous spaces

Author(s) -

Dmitry Kleinbock,

Gregori Aleksandrovitch Margulis

Publication year - 1995

Publication title -

translations - american mathematical society/translations

Language(s) - English

Resource type - Reports

eISSN - 2472-3193

pISSN - 0065-9290

DOI - 10.1090/trans2/171/11

Subject(s) - lie group , homogeneous , mathematics , bounded function , hausdorff dimension , pure mathematics , lattice (music) , hausdorff space , group (periodic table) , combinatorics , mathematical analysis , physics , quantum mechanics , acoustics

Let {gt} be a nonquasiunipotent one-parameter subgroup of a connected semisimple Lie group G without compact factors; we prove that the set of points in a homogeneous spaceG/Γ (Γ an irreducible lattice inG) with bounded {gt}-trajectories has full Hausdorff dimension. Using this we give necessary and sufficient conditions for this property to hold for any Lie group G and any lattice Γ in G.

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