Power spectrum of the geodesic flow on hyperbolic manifolds
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Author(s)
Faure, Frédéric
Guillarmou, Colin
Dyatlov, Semen
Date Issued
June 2015
Journal
Analysis & PDE
Publisher
Mathematical Sciences Publishers
Citation
Dyatlov, Semyon, Frédéric Faure, and Colin Guillarmou. “Power Spectrum of the Geodesic Flow on Hyperbolic Manifolds.” Analysis & PDE 8, no. 4 (June 21, 2015): 923–1000.
Version
Author's final manuscript
Abstract
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.
Subjects
Pollicott–Ruelle resonances, hyperbolic manifolds
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.2140/APDE.2015.8.923
