{
  "id": "2205.09002",
  "version": "v1",
  "published": "2022-05-18T15:33:52.000Z",
  "updated": "2022-05-18T15:33:52.000Z",
  "title": "Oriented and standard shadowing properties for topological flows",
  "authors": [
    "Sogo Murakami"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that oriented and standard shadowing properties are equivalent for topological flows with finite singularites that are Lyapunov stable or Lyapunov unstable. Moreover, we prove that the direct product $\\phi_1 \\times \\phi_2$ of two topological flows has the oriented shdowing property if $\\phi_1$ with finite singuralities has the oriented shadowing property, while $\\phi_2$ has the limit set consisting of finite singularities that are Lyapunov stable or Lyapunov unstable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-18T15:33:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B65",
      "37C10"
    ],
    "keywords": [
      "standard shadowing properties",
      "topological flows",
      "finite singularities",
      "lyapunov stable",
      "lyapunov unstable"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}