Resonances for Normally Hyperbolic Trapped Sets

Resonances for Normally Hyperbolic Trapped Sets - Semyon Dyatlov

Semyon Dyatlov
University of California
April 2, 2013

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.