Homogeneous orbit closures and applications

Elon Lindenstrauss*, Uri Shapira

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We give new classes of examples of orbits of the diagonal group in the space of unit volume lattices in R d 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 iminf |n|→∞|n|√ 32-γn 34- δ=0, where denotes the distance of a real number c to the integers.

Original languageAmerican English
Pages (from-to)785-807
Number of pages23
JournalErgodic Theory and Dynamical Systems
Volume32
Issue number2
DOIs
StatePublished - Apr 2012

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