{
  "id": "0809.0277",
  "version": "v1",
  "published": "2008-09-01T16:46:05.000Z",
  "updated": "2008-09-01T16:46:05.000Z",
  "title": "Structural stability of attractor-repellor endomorphisms with singularities",
  "authors": [
    "Pierre Berger"
  ],
  "comment": "37 pages",
  "categories": [
    "math.DS",
    "math.DG"
  ],
  "abstract": "We prove a theorem on structural stability of smooth attractor-repellor endomorphisms of compact manifolds, with singularities. By attractor-repellor, we mean that the non-wandering set of the dynamics $f$ is the disjoint union of a repulsive compact subset with a hyperbolic attractor on which $f$ acts bijectively. The statement of this result is both infinitesimal and dynamical. Up to our knowledge, this is the first in this hybrid direction. Our results generalize also a Mather's theorem in singularity theory which states that infinitesimal stability implies structural stability for composed mappings, to the larger category of laminations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-01T16:46:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singularity",
      "infinitesimal stability implies structural stability",
      "smooth attractor-repellor endomorphisms",
      "disjoint union",
      "compact manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.0277B"
    }
  }
}