TY - JOUR
T1 - Homogeneous orbit closures and applications
AU - Lindenstrauss, Elon
AU - Shapira, Uri
PY - 2012/4
Y1 - 2012/4
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84858638665&partnerID=8YFLogxK
U2 - 10.1017/S0143385710000842
DO - 10.1017/S0143385710000842
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AN - SCOPUS:84858638665
SN - 0143-3857
VL - 32
SP - 785
EP - 807
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 2
ER -