Partie 2/2 -
Hyperbolic dispersive estimates, topological pressure, and applications
par Maciej Zworski (Berkeley University)
Séminaire d'analyse IHP-Fondation Sciences Mathématiques de Paris
Conférence du lundi 7 février 2011
Following the work of Anantharaman and Nonnenmacher, Nonnenmacher and the speaker developed estimates for semiclassical propagators for open chaotic systems: under conditions on the topological pressure of the classical system one obtains exponential decay in time. This gives resonance free strips, resolvent estimates, local smoothing estimates. In related work of Wunsch and the speaker similar estimates are obtained for normally hyperbolic trapped sets. Dyatlov applied these to quasinormal modes for black holes which gives exponential decay of linear waves in Kerr-deSitter background.