Power spectrum of the geodesic flow on hyperbolic manifolds
Power spectrum of the geodesic flow on hyperbolic manifolds
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双曲流形上测地流的功率谱
DOI：
10.2140/apde.2015.8.923
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
C. Guillarmou
中科院分区：
文献类型：
--
作者：
S. Dyatlov;F. Faure;C. Guillarmou
我们用作用于某些自然张量束的拉普拉斯本征值描述紧致双曲流形上测地线流的相关功率谱的复极点。这些极点是波利柯-鲁埃尔共振的一种特殊情况，它可以定义为一般的阿诺索夫流。在我们的例子中，共振根据衰减率分层成带。证明还给出了拉普拉斯算子的共振态与本征态之间的显式关系。
We describe the complex poles of the power spectrum of correlations for the geodesic flow on compact hyperbolic manifolds in terms of eigenvalues of the Laplacian acting on certain natural tensor bundles. These poles are a special case of Pollicott-Ruelle resonances, which can be defined for general Anosov flows. In our case, resonances are stratified into bands by decay rates. The proof also gives an explicit relation between resonant states and eigenstates of the Laplacian.