TY - JOUR
T1 - Invariant measures and arithmetic quantum unique ergodicity
AU - Lindenstrauss, Elon
PY - 2006
Y1 - 2006
N2 - We classify measures on the locally homogeneous space Γ\ SL(2, ℝ) × L which are invariant and have positive entropy under the diagonal subgroup of SL(2, ℝ) and recurrent under L. This classification can be used to show arithmetic quantum unique ergodicity for compact arithmetic surfaces, and a similar but slightly weaker result for the finite volume case. Other applications are also presented. In the appendix, joint with D. Rudolph, we present a maximal ergodic theorem, related to a theorem of Hurewicz, which is used in theproof of the main result.
AB - We classify measures on the locally homogeneous space Γ\ SL(2, ℝ) × L which are invariant and have positive entropy under the diagonal subgroup of SL(2, ℝ) and recurrent under L. This classification can be used to show arithmetic quantum unique ergodicity for compact arithmetic surfaces, and a similar but slightly weaker result for the finite volume case. Other applications are also presented. In the appendix, joint with D. Rudolph, we present a maximal ergodic theorem, related to a theorem of Hurewicz, which is used in theproof of the main result.
UR - http://www.scopus.com/inward/record.url?scp=33644586868&partnerID=8YFLogxK
U2 - 10.4007/annals.2006.163.165
DO - 10.4007/annals.2006.163.165
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AN - SCOPUS:33644586868
SN - 0003-486X
VL - 163
SP - 165
EP - 219
JO - Annals of Mathematics
JF - Annals of Mathematics
IS - 1
ER -