Dyatlov, S;
Galkowski, J;
(2017)
Fractal Weyl laws and wave decay for general trapping.
Nonlinearity
, 30
(12)
, Article 4301. 10.1088/1361-6544/aa8712.
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Abstract
We prove a Weyl upper bound on the number of scattering resonances in strips for manifolds with Euclidean infinite ends. In contrast with previous results, we do not make any strong structural assumptions on the geodesic flow on the trapped set (such as hyperbolicity) and instead use propagation statements up to the Ehrenfest time. By a similar method we prove a decay statement with high probability for linear waves with random initial data. The latter statement is related heuristically to the Weyl upper bound. For geodesic flows with positive escape rate, we obtain a power improvement over the trivial Weyl bound and exponential decay up to twice the Ehrenfest time.
| Type: | Article |
|---|---|
| Title: | Fractal Weyl laws and wave decay for general trapping |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1088/1361-6544/aa8712 |
| Publisher version: | https://doi.org/10.1088/1361-6544/aa8712 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | resonances, Weyl law, wave decay Mathematics Subject Classification numbers: 35B34 |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10083904 |
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