### Citation:

Iantchenko , A 2007 , ' Scattering poles near the real axis for two strictly convex obstacles ' Annales Henri Poincaré , vol 8 , no. 3 , pp. 513-568 . DOI: 10.1007/s00023-006-0315-3

### 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.

### Description:

Iantchenko, A., (2007) 'Scattering poles near the real axis for two strictly convex obstacles', Annales of the Institute Henri Poincaré 8 pp.513-568 RAE2008