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2015 Power spectrum of the geodesic flow on hyperbolic manifolds
Semyon Dyatlov, Frédéric Faure, Colin Guillarmou
Anal. PDE 8(4): 923-1000 (2015). DOI: 10.2140/apde.2015.8.923

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.

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Semyon Dyatlov. Frédéric Faure. Colin Guillarmou. "Power spectrum of the geodesic flow on hyperbolic manifolds." Anal. PDE 8 (4) 923 - 1000, 2015. https://doi.org/10.2140/apde.2015.8.923

Information

Received: 28 October 2014; Revised: 30 January 2015; Accepted: 6 March 2015; Published: 2015
First available in Project Euclid: 16 November 2017

zbMATH: 1371.37056
MathSciNet: MR3366007
Digital Object Identifier: 10.2140/apde.2015.8.923

Subjects:
Primary: 37D40

Keywords: hyperbolic manifolds , Pollicott–Ruelle resonances

Rights: Copyright © 2015 Mathematical Sciences Publishers

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