{
  "id": "1706.01266",
  "version": "v1",
  "published": "2017-06-05T10:45:23.000Z",
  "updated": "2017-06-05T10:45:23.000Z",
  "title": "On chaotic behavior of the $P$-adic generalized Ising mapping and its application",
  "authors": [
    "Farrukh Mukhamedov",
    "Hasan Akin",
    "Mutlay Dogan"
  ],
  "comment": "16 pages, Journal of Difference Equations and Applications (accepted)",
  "categories": [
    "math.DS"
  ],
  "abstract": "In the present paper, by conducting research on the dynamics of the $p$-adic generalized Ising mapping corresponding to renormalization group associated with the $p$-adic Ising-Vannemenus model on a Cayley tree, we have determined the existence of the fixed points of a given function. Simultaneously, the attractors of the dynamical system have been found. We have come to a conclusion that the considered mapping is topologically conjugate to the symbolic shift which implies its chaoticity and as an application, we have established the existence of periodic $p$-adic Gibbs measures for the $p$-adic Ising-Vannemenus model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-05T10:45:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46S10",
      "82B26",
      "12J12",
      "39A70",
      "47H10",
      "60K35"
    ],
    "keywords": [
      "adic generalized ising mapping",
      "chaotic behavior",
      "adic ising-vannemenus model",
      "application",
      "generalized ising mapping corresponding"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}