{
  "id": "2402.05433",
  "version": "v1",
  "published": "2024-02-08T06:11:16.000Z",
  "updated": "2024-02-08T06:11:16.000Z",
  "title": "A note on the hyperbolicity of the non-wandering sets of real quadratic maps",
  "authors": [
    "Diyath Pannipitiya"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "The goal of this paper is to discuss about the hyperbolicity of the non-wandering set $\\mathcal{NW}(f_c)$ of real quadratic function $f_c(x)=x^2+c$ when $c\\in (-\\infty, -2]$. Even though the results we present here are not new, it is not easier to find the proofs of them. We present two different ways to prove the hyperbolicity of $\\mathcal{NW}(f_c)$ for the``considerably difficult case'' of when $c$ is closer to $-2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-02-08T06:11:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "real quadratic maps",
      "non-wandering set",
      "hyperbolicity",
      "real quadratic function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}