{
  "id": "math/0501172",
  "version": "v1",
  "published": "2005-01-11T21:01:33.000Z",
  "updated": "2005-01-11T21:01:33.000Z",
  "title": "Longitudinal KAM-cocycles and action spectra of magnetic flows",
  "authors": [
    "Nurlan S. Dairbekov Gabriel P. Paternain"
  ],
  "categories": [
    "math.DS",
    "math.DG"
  ],
  "abstract": "Let $M$ be a closed oriented surface and let $\\Omega$ be a non-exact 2-form. Suppose that the magnetic flow $\\phi$ of the pair $(g,\\Omega)$ is Anosov. We show that the longitudinal KAM-cocycle of $\\phi$ is a coboundary if and only the Gaussian curvature is constant and $\\Omega$ is a constant multiple of the area form thus extending the results in \\cite{P2}. We also show infinitesimal rigidity of the action spectrum of $\\phi$ with respect to variations of $\\Omega$. Both results are obtained by showing that if $G:M\\to\\mathbb R$ is any smooth function and $\\omega$ is any smooth 1-form on $M$ such that $G(x)+\\omega_{x}(v)$ integrates to zero along any closed orbit of $\\phi$, then $G$ must be identically zero and $\\omega$ must be exact.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-01-11T21:01:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "magnetic flow",
      "longitudinal kam-cocycle",
      "action spectrum",
      "constant multiple",
      "area form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......1172P"
    }
  }
}