{
  "id": "math/0702022",
  "version": "v1",
  "published": "2007-02-01T16:09:19.000Z",
  "updated": "2007-02-01T16:09:19.000Z",
  "title": "Scattering Poles Near the Real Axis for Two Strictly Convex Obstacles",
  "authors": [
    "Alexei Iantchenko"
  ],
  "doi": "10.1007/s00023-006-0315-3",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "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 Ikawa and G{\\'e}rard established the existence of parallel rows of poles in a strip $Im z\\leq c$ as $Re z$ tends to infinity. Assuming that the boundaries are analytic and the eigenvalues of Poincar{\\'e} map are non-resonant we use the Birkhoff normal form for $M$ to improve this result and to get the complete asymptotic expansions for the poles in any logarithmic neighborhood of real axis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-02-01T16:09:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "strictly convex obstacles",
      "real axis",
      "scattering poles",
      "complete asymptotic expansions",
      "birkhoff normal form"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007AnHP....8..513I"
    }
  }
}