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.