Invariant measures and arithmetic quantum unique ergodicity

• 成果类型: Article
• 署名作者: Lindenstrauss, Elon
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2006.163.165
• 发表日期: 2006
• 页码: 165-219
• 关键词: uniform-distribution; unipotent subgroups; measure rigidity; entropy; conjectures; THEOREM; sets

摘要

We classify measures on the locally homogeneous space Gamma\SL(2, R) x 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.