{
  "id": "2412.11221",
  "version": "v2",
  "published": "2024-12-15T15:26:47.000Z",
  "updated": "2025-01-26T16:28:21.000Z",
  "title": "Shadowing property for set-valued map and its inverse limit",
  "authors": [
    "Zhengyu Yin"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this article, we investigate the relationship between the shadowing property of set-valued maps and their associated inverse limit systems. We show that if a set-valued map is expansive and open in the context of set-valued dynamics, then certain induced inverse limit systems have the shadowing property. Additionally, we prove that a continuous set-valued map has the shadowing property if and only if some of its induced inverse limit system also has shadowing property. Finally, we establish that the shadowing property of a set-valued map is equivalent to the shadowing property of its induced inverse set-valued system.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-01-26T16:28:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "shadowing property",
      "induced inverse limit system",
      "associated inverse limit systems",
      "induced inverse set-valued system",
      "continuous set-valued map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}