Analysis & PDE
- Anal. PDE
- Volume 8, Number 4 (2015), 923-1000.
Power spectrum of the geodesic flow on hyperbolic manifolds
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.
Anal. PDE, Volume 8, Number 4 (2015), 923-1000.
Received: 28 October 2014
Revised: 30 January 2015
Accepted: 6 March 2015
First available in Project Euclid: 16 November 2017
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Dyatlov, Semyon; Faure, Frédéric; Guillarmou, Colin. Power spectrum of the geodesic flow on hyperbolic manifolds. Anal. PDE 8 (2015), no. 4, 923--1000. doi:10.2140/apde.2015.8.923. https://projecteuclid.org/euclid.apde/1510843117