POWER SPECTRUM OF THE GEODESIC FLOW ON HYPERBOLIC MANIFOLDS

被引：45

作者：

Dyatlov, Semyon ^{[1
]}

Faure, Frederic ^{[2
]}

Guillarmou, Colin ^{[3
]}

机构：

[1] MIT, Dept Math, Cambridge, MA 02139 USA

[2] Univ Joseph Fourier, Inst Fourier, F-38402 St Martin Dheres, France

[3] Ecole Normale Super, CNRS, DMA, UMR 8553, F-75230 Paris, France

来源：

ANALYSIS & PDE | 2015年 / 8卷 / 04期

关键词：

Pollicott-Ruelle resonances; hyperbolic manifolds; SELBERG ZETA-FUNCTION; ANOSOV-FLOWS; EIGENFUNCTIONS; INVARIANT; DISTRIBUTIONS; LAPLACIAN; OPERATORS; SPACES; DECAY;

D O I：

10.2140/apde.2015.8.923

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：923 / 1000

页数：78

共 55 条

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Abramowitz M., 1964, NBS APPL MATH SERIES, V55

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