Analysis & PDE

  • Anal. PDE
  • Volume 8, Number 4 (2015), 923-1000.

Power spectrum of the geodesic flow on hyperbolic manifolds

Semyon Dyatlov, Frédéric Faure, and Colin Guillarmou

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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.

Article information

Source
Anal. PDE, Volume 8, Number 4 (2015), 923-1000.

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

Permanent link to this document
https://projecteuclid.org/euclid.apde/1510843117

Digital Object Identifier
doi:10.2140/apde.2015.8.923

Mathematical Reviews number (MathSciNet)
MR3366007

Zentralblatt MATH identifier
1371.37056

Subjects
Primary: 37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)

Keywords
Pollicott–Ruelle resonances hyperbolic manifolds

Citation

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


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