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Power spectrum of the
geodesic flow on hyperbolic manifolds
Semyon Dyatlov, Frédéric Faure and Colin Guillarmou |
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Vol. 8 (2015), No. 4, 923–1000
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Abstract |
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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. |
Keywords
Pollicott–Ruelle resonances, hyperbolic manifolds
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Mathematical Subject Classification 2010
Primary: 37D40
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Milestones
Received: 28 October 2014
Revised: 30 January 2015
Accepted: 6 March 2015
Published: 21 June 2015
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Authors |
| Semyon Dyatlov | |
| Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 02139 United States |
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| Frédéric Faure | |
| Institut Fourier Universite Joseph Fourier 100, rue des Maths, BP74 38402 St Martin d’Heres France |
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| Colin Guillarmou | |
| DMA, U.M.R. 8553 CNRS École Normale Supérieure 45 rue d’Ulm, DMA 75230 Paris France |
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