89 citations · 1.1k across the 43 of their papers we have counts for
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Pollicott-Ruelle resonances for open systems
Semyon Dyatlov, Colin Guillarmou
We define Pollicott-Ruelle resonances for geodesic flows on noncompact asymptotically hyperbolic negatively curved manifolds, as well as for more general open hyperbolic systems re…
Stochastic stability of Pollicott-Ruelle resonances
Semyon Dyatlov, Maciej Zworski
Pollicott-Ruelle resonances for chaotic flows are the characteristic frequencies of correlations. They are typically defined as eigenvalues of the generator of the flow acting on s…
Spectral gaps for normally hyperbolic trapping
Semyon Dyatlov
We establish a resonance free strip for codimension 2 symplectic normally hyperbolic trapped sets with smooth incoming/outgoing tails. An important application is wave decay on Ker…
Power spectrum of the geodesic flow on hyperbolic manifolds
Semyon Dyatlov, Frédéric Faure, Colin Guillarmou
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…
Resonances and lower resolvent bounds
Kiril Datchev, Semyon Dyatlov, Maciej Zworski
We show how the presence of resonances close to the real axis implies exponential lower bounds on the norm of the cut-off resolvent on the real axis.