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Power spectrum of the geodesic flow on hyperbolic manifolds

Author(s)
Faure, Frédéric; Guillarmou, Colin; Dyatlov, Semen
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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.
Date issued
2015-06
URI
http://hdl.handle.net/1721.1/115962
Department
Massachusetts Institute of Technology. Department of Mathematics
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
ISSN
2157-5045
Keywords
Pollicott–Ruelle resonances, hyperbolic manifolds

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