{
  "id": "1612.04752",
  "version": "v1",
  "published": "2016-12-14T17:56:49.000Z",
  "updated": "2016-12-14T17:56:49.000Z",
  "title": "Splitting of separatrices in a family of area-preserving maps that unfolds a fixed point at the resonance of order three",
  "authors": [
    "Giannis Moutsinas"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the exponentially small splitting of separatrices in an one parameter family of area-preserving maps that unfolds the 1:3 resonance. We show that under a certain non-degeneracy condition we can compute a Stokes constant $\\theta$ for the map. When this constant is non zero, we provide an asymptotic for the splitting of separatrices for the map.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-14T17:56:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "area-preserving maps",
      "fixed point",
      "separatrices",
      "non-degeneracy condition",
      "stokes constant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}