Power spectrum of the geodesic flow on hyperbolic manifolds
Author(s)Faure, Frédéric; Guillarmou, Colin; Dyatlov, Semen
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Analysis & PDE
Mathematical Sciences Publishers
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.
Author's final manuscript
Pollicott–Ruelle resonances, hyperbolic manifolds