Resonances for Normally Hyperbolic Trapped Sets
| Analysis Seminar | |
| Topic: | Resonances for Normally Hyperbolic Trapped Sets |
| Speaker: | Semyon Dyatlov |
| Affiliation: | University of California |
| Date: | Tuesday, April 2 |
| Time/Room: | 3:15pm - 4:15pm/S-101 |
Resonances are complex analogs of eigenvalues for Laplacians on noncompact manifolds, arising in long time resonance expansions of linear waves. We prove a Weyl type asymptotic formula for the number of resonances in a strip, provided that the set of trapped geodesics is r-normally hyperbolic for large r and satisfies a pinching condition. Our dynamical assumptions are stable under small smooth perturbations and motivated by applications to black holes. We also establish a high frequency analog of resonance expansions.