Resonance projectors and asymptotics for r -normally hyperbolic trapped sets
By Semyon Dyatlov. 2013
49 citations recorded by the source corpus.
We prove an asymptotic formula for the number of scattering resonances in a strip near the real axis when the trapped set is r-normally hyperbolic with r large and a pinching condition on the normal expansion rates holds. Our dynamical assumptions are stable under smooth perturbations and motivated by the setting of black holes. The key tool is a Fourier integral operator which microlocally projects onto the resonant states in the strip. In addition to Weyl law, this operator provides new information about microlocal concentration of resonant states.
Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/d756347b7e0dc6e7acd86a8427f7a64e31631d04
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In Applied Mathematics
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Fractal Weyl laws for asymptotically hyperbolic manifolds (2012, methodology): “Most recently, Weyl asymptotics for resonances in strips have been obtained under more restrictive dynamical assumptions in work in preparation by Faure and Tsuji [FT] and the second author [Dya].”
- The semiclassical zeta function for geodesic flows on negatively curved manifolds (2013, background): “We would like to mention also a closely related work: in [10], for a problem concerning decay of waves around black holes, S.”