Homogeneous orbit closures and applications
نویسندگان
چکیده
منابع مشابه
Homogeneous Orbit Closures and Applications
We give new classes of examples of orbits of the diagonal group in the space of unit volume lattices in R for d ≥ 3 with nice (homogeneous) orbit closures, as well as examples of orbits with explicitly computable but irregular orbit closures. We give Diophantine applications to the former, for instance we show that for all γ, δ ∈ R lim inf |n|→∞ |n| 〈n 3 √ 2− γ〉〈n 3 √ 4− δ〉 = 0, where 〈c〉 denot...
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The theorems of M. Ratner, describing the finite ergodic invariant measures and the orbit closures for unipotent flows on homogeneous spaces of Lie groups, are extended for actions of subgroups generated by unipotent elements. More precisely: Let G be a Lie group (not necessarily connected) and Γ a closed subgroup of G. Let W be a subgroup of G such that AdG(W ) is contained in the Zariski clos...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2011
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385710000842