Scattering poles near the real axis for two strictly convex obstacles

A. Iantchenko

Research output: Contribution to journalArticlepeer-review

4 Citations (SciVal)

Abstract

To study the location of poles for the acoustic scattering matrix for two strictly convex obstacles with smooth boundaries, one uses an approximation of the quantized billiard operator M along the trapped ray between the two obstacles. Using this method Gérard (cf. [7]) obtained complete asymptotic expansions for the poles in a strip Im z ≤ c as Re z tends to infinity. He established the existence of parallel rows of poles close to Assuming that the boundaries are analytic and the eigenvalues of Poincaré map are non-resonant we use the Birkhoff normal form for M to improve his result and to get the complete asymptotic expansions for the poles in any logarithmic neighborhood of real axis.
Original languageEnglish
Pages (from-to)513-568
Number of pages56
JournalAnnales Henri Poincaré
Volume8
Issue number3
DOIs
Publication statusPublished - Jun 2007

Fingerprint

Dive into the research topics of 'Scattering poles near the real axis for two strictly convex obstacles'. Together they form a unique fingerprint.

Cite this