Propagation through trapped sets and semiclassical resolvent estimates

Datchev, Kiril; Vasy, András

Annales de l'Institut Fourier, Tome 62 (2012) no. 6, pp. 2347-2377.

Motivé par l’étude des estimations de la résolvante dans la présence de capture, on démontre un théorème de propagation semiclassique dans un voisinage d’un sous-ensemble compact et invariant du flôt bicaractéristique, qui est isolé dans un sens convenable. Les exemples incluent un ensemble capté global et une trajectoire périodique isolée. Ceci est appliqué pour obtenir des estimations microlocales de la résolvante sans perte par rapport au cas non-captif.

Motivated by the study of resolvent estimates in the presence of trapping, we prove a semiclassical propagation theorem in a neighborhood of a compact invariant subset of the bicharacteristic flow which is isolated in a suitable sense. Examples include a global trapped set and a single isolated periodic trajectory. This is applied to obtain microlocal resolvent estimates with no loss compared to the nontrapping setting.

Classification : 58J47, 35L05
Keywords: Resolvent estimates, trapping, propagation of singularities.
Mot clés : Estimations de résolvantes, ensembles captifs, propagation de singularités

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