Stochastic Stability of Pollicott–Ruelle Resonances

Kinetic Brownian motion on the cosphere bundle of a Riemannian manifold M is a stochastic process that models the geodesic equation perturbed by a random white force of size ε . When M is compact and negatively curved, we show that the L 2 -spectrum of the infinitesimal generator of this process con...

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Veröffentlicht in:	Communications in mathematical physics 2017-12, Vol.356 (2), p.357-396
1. Verfasser:	Drouot, Alexis
Format:	Artikel
Sprache:	eng
Schlagworte:	Brownian motion Classical and Quantum Gravitation Complex Systems Mathematical and Computational Physics Mathematical Physics Motion stability Physics Physics and Astronomy Quantum Physics Relativity Theory Riemann manifold Theoretical
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Beschreibung
Zusammenfassung:	Kinetic Brownian motion on the cosphere bundle of a Riemannian manifold M is a stochastic process that models the geodesic equation perturbed by a random white force of size ε . When 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 M as ε goes to 0.
ISSN:	0010-3616 1432-0916
DOI:	10.1007/s00220-017-2956-0