{
  "id": "2111.01927",
  "version": "v2",
  "published": "2021-11-02T22:31:07.000Z",
  "updated": "2025-01-03T15:42:43.000Z",
  "title": "Porosities of the sets of attractors",
  "authors": [
    "Paweł Klinga",
    "Adam Kwela"
  ],
  "categories": [
    "math.DS",
    "math.GN"
  ],
  "abstract": "This paper is another attempt to measure the difference between the family $A[0,1]$ of attractors for iterated function systems acting on $[0,1]$ and a broader family, the set $A_w[0,1]$ of attractors for weak iterated function systems acting on $[0,1]$. It is known that both $A[0,1]$ and $A_w[0,1]$ are meager subsets of the hyperspace $K([0,1])$ (of all compact subsets of $[0,1]$ equipped in the Hausdorff metric). Actually, $A[0,1]$ is even $\\sigma$-lower porous while the question about $\\sigma$-lower porosity of $A_w[0,1]$ is still open. We prove that $A[0,1]$ is not $\\sigma$-strongly porous in $K([0,1])$. Moreover, we show that $A_w[0,1]\\setminus A[0,1]$ is dense in $K([0,1])$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-01-03T15:42:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "attractors",
      "lower porosity",
      "hausdorff metric",
      "compact subsets",
      "meager subsets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}