Propagation through trapped sets and semiclassical resolvent estimates

Understand

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.