{
  "id": "0806.1502",
  "version": "v4",
  "published": "2008-06-09T17:36:44.000Z",
  "updated": "2015-12-24T13:20:27.000Z",
  "title": "Local inverses of shift maps along orbits of flows",
  "authors": [
    "Sergiy Maksymenko"
  ],
  "comment": "43 pages, 4 figures. V3. The class of admissible singularities for vector field is extended",
  "journal": "Osaka Journal of Mathematics, vol. 48, no. 2 (2011) 415-455",
  "categories": [
    "math.DS",
    "math.GT"
  ],
  "abstract": "Let $M$ be a smooth manifold and $F$ be a vector field on $M$. My article [\"Smooth shifts along trajectories of flows\", Topol. Appl. 130 (2003) 183-204, arXiv:math/0106199] concerning the homotopy types of the group of diffeomorphisms preserving orbits of $F$ contains two errors. They imply that the principal statement of that paper holds under additional assumptions on $F$. Unfortunately this result was essentially used in another paper of mine [\"Homotopy types of stabilizers and orbits of Morse functions on surfaces\" Ann. Glob. Anal. Geom., 29 no. 3, (2006) 241-285, arXiv:math/0310067]. The aim of this article is to expose the results of the first paper in a right way, extend them to a larger class of flows with degenerate singularities, and show that the results of the second paper remain true.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-12-17T13:35:09.000Z",
      "abstract": "Let M be a smooth manifold and F be a vector field on $M$. My article [\"Smooth shifts along trajectories of flows\", Topol. Appl. 130 (2003) 183-204, arXiv:math/0106199] concerning the homotopy types of the group of diffeomorphisms preserving orbits of F contains two errors. They imply that the principal statement of that paper holds under additional assumptions on F. Unfortunately this result was essentially used in another paper of mine [\"Homotopy types of stabilizers and orbits of Morse functions on surfaces\" Ann. Glob. Anal. Geom., 29 no. 3, (2006) 241-285, arXiv:math/0310067]. The aim of this article is to expose the results of the first paper in a right way, extend them to a larger class of flows with degenerate singularities, and show that the results of the second paper remain true.",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-12-24T13:20:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C05",
      "57S05",
      "57R45"
    ],
    "keywords": [
      "shift maps",
      "local inverses",
      "second paper remain true",
      "homotopy types",
      "smooth shifts"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.1502M"
    }
  }
}