{
  "id": "2303.06131",
  "version": "v1",
  "published": "2023-03-10T18:49:50.000Z",
  "updated": "2023-03-10T18:49:50.000Z",
  "title": "On the Shadowableness of Flows With Hyperbolic Singularities",
  "authors": [
    "Alexander Arbieto",
    "Andrés M. López",
    "Elias Rego",
    "Yeison Sánchez"
  ],
  "comment": "18 pages, 3 figures",
  "doi": "10.1007/s00208-023-02767-8",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this work we study the existence of singular flows satisfying shadowing-like properties. More precisely, we prove that if C1 -vector field on a closed manifold induces a chain-recurrent flow containing an attached hyperbolic singularity of stable or unstable index-one, then this flow cannot satisfy the shadowing property. If the manifold is non-compact, the vector field is complete and non-wandering, we prove that we prove that the existence of index-one hyperbolic singularities prevents the induced flow to satisfy the rescaled-shadowing property introduced in [6].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-10T18:49:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C10",
      "37C50"
    ],
    "keywords": [
      "vector field",
      "index-one hyperbolic singularities prevents",
      "shadowableness",
      "singular flows satisfying shadowing-like properties",
      "chain-recurrent flow"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}