Propagation through trapped sets and semiclassical resolvent estimates

Details Propagation through trapped sets and semiclassical resolvent estimates Propagation through trapped sets and semiclassical resolvent estimates

2010-10-11

arxiv.org/abs/1010.2190v1

Mathematics

Analysis of PDEs

22 pages, 6 figures

Scientific paper

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.

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