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Homogeneous orbit closures and applications
Published online by Cambridge University Press: 28 April 2011
Abstract
We give new classes of examples of orbits of the diagonal group in the space of unit volume lattices in ℝd 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, where 〈c〉 denotes the distance of a real number c to the integers.
- Type
- Research Article
- Information
- Ergodic Theory and Dynamical Systems , Volume 32 , Issue 2: Daniel J. Rudolph – in Memoriam , April 2012 , pp. 785 - 807
- Copyright
- Copyright © Cambridge University Press 2011
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