Invariant measures and arithmetic quantum unique ergodicity
Invariant measures and arithmetic quantum unique ergodicity
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DOI：
10.4007/annals.2006.163.165
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发表时间：
2006-01-01
影响因子：
4.9
通讯作者：
Lindenstrauss, Elon
中科院分区：
文献类型：
--
作者：
Lindenstrauss, Elon
我们对局部齐性空间Gamma\SL（2，R）x L上的测度进行分类，这些测度在SL（2，R）的对角子群下是不变的，具有正熵，在L下是常返的.这种分类可以用来显示紧凑算术表面的算术量子唯一遍历性，以及有限体积情况下的类似但稍弱的结果。在附录中，结合D. Rudolph，我们给出了一个极大遍历定理，它与Hurewicz的一个定理有关，并用于主要结果的证明.
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.