{
  "id": "1511.04363",
  "version": "v1",
  "published": "2015-11-12T06:59:08.000Z",
  "updated": "2015-11-12T06:59:08.000Z",
  "title": "Dynamics of $\\displaystyle{z_{n+1}=\\frac{α+ αz_{n}+β z_{n-1}}{1+z_{n}}}$ in Complex Plane",
  "authors": [
    "Sk. Sarif Hassan"
  ],
  "comment": "Initial Draft. arXiv admin note: substantial text overlap with arXiv:1509.00850",
  "categories": [
    "math.DS"
  ],
  "abstract": "The dynamics of the second order rational difference equation $\\displaystyle{z_{n+1}=\\frac{\\alpha + \\alpha z_{n}+\\beta z_{n-1}}{1+z_{n}}}$ with complex parameters $\\alpha$, $\\beta$ and arbitrary complex initial conditions is investigated. The same difference equation is well studied with positive real parameters and initial values and one of the main results on trichotomy of parameters is revisited in the complex set-up and the similar result is found to be true. In addition, the chaotic solutions of the equation is fetched out in the complex set-up which was absent in the real scenario.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-12T06:59:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex plane",
      "second order rational difference equation",
      "complex set-up",
      "arbitrary complex initial conditions",
      "complex parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}