{
  "id": "math-ph/0206027",
  "version": "v2",
  "published": "2002-06-17T21:37:34.000Z",
  "updated": "2004-02-10T20:38:11.000Z",
  "title": "Hamiltonian and Linear-Space Structure for Damped Oscillators: II. Critical Points",
  "authors": [
    "S. C. Chee",
    "Alec Maassen van den Brink",
    "K. Young"
  ],
  "comment": "REVTeX4, 9pp., 5 PS figures. v2: extensive streamlining",
  "journal": "J. Phys. A _37_, 8883 (2004)",
  "doi": "10.1088/0305-4470/37/37/009",
  "categories": [
    "math-ph",
    "math.DS",
    "math.MP",
    "math.RA",
    "physics.class-ph"
  ],
  "abstract": "The eigenvector expansion developed in the preceding paper for a system of damped linear oscillators is extended to critical points, where eigenvectors merge and the time-evolution operator $H$ assumes a Jordan-block structure. The representation of the bilinear map is obtained in this basis. Perturbations $\\epsilon\\Delta H$ around an $M$-th order critical point generically lead to eigenvalue shifts $\\sim\\epsilon^{1/M}$ dependent on only_one_ matrix element, with the $M$ eigenvalues splitting in equiangular directions in the complex plane. Small denominators near criticality are shown to cancel.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-02-10T20:38:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear-space structure",
      "damped oscillators",
      "hamiltonian",
      "bilinear map",
      "small denominators"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2004,
      "month": "Sep",
      "volume": 37,
      "pages": 8883
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004JPhA...37.8883C"
    }
  }
}