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Stochastic Stability of Pollicott–Ruelle Resonances

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Abstract

Kinetic Brownian motion on the cosphere bundle of a Riemannian manifold \({\mathbb{M}}\) is a stochastic process that models the geodesic equation perturbed by a random white force of size \({\varepsilon}\). When \({\mathbb{M}}\) is compact and negatively curved, we show that the L 2-spectrum of the infinitesimal generator of this process converges to the Pollicott–Ruelle resonances of \({\mathbb{M}}\) as \({\varepsilon}\) goes to 0.

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Authors and Affiliations

  1. University of California Berkeley, Berkeley, CA, USA

    Alexis Drouot

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  1. Alexis Drouot
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Correspondence to Alexis Drouot.

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Communicated by J. Marklof

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Drouot, A. Stochastic Stability of Pollicott–Ruelle Resonances. Commun. Math. Phys. 356, 357–396 (2017). https://doi.org/10.1007/s00220-017-2956-0

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  • DOI: https://doi.org/10.1007/s00220-017-2956-0

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