{
  "id": "2312.01312",
  "version": "v1",
  "published": "2023-12-03T07:47:36.000Z",
  "updated": "2023-12-03T07:47:36.000Z",
  "title": "A note on chaotic billiards with potentials",
  "authors": [
    "Vivina L. Barutello",
    "Irene De Blasi"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In arXiv:2212.01150, the authors provide a sufficient purely geometrical condition on a planar billiard containing a Keplerian center that ensures the chaoticity of the model. This note is intended as a continuation of the analysis in arXiv:2212.01150 in the sense that it provides an investigation of the actual holding of such a condition, starting from the case of an elliptic billiard. Our main result states that an elliptic (but not circular) domain with a Keplerian mass situated almost everywhere in its interior presents a chaotic dynamics both in reflective and refractive models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-03T07:47:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "chaotic billiards",
      "potentials",
      "main result states",
      "chaotic dynamics",
      "keplerian center"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}