{
  "id": "1011.3836",
  "version": "v1",
  "published": "2010-11-16T21:35:46.000Z",
  "updated": "2010-11-16T21:35:46.000Z",
  "title": "Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms",
  "authors": [
    "Sylvain Crovisier",
    "Enrique R. Pujals"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that any diffeomorphism of a compact manifold can be approximated in topology C1 by another diffeomorphism exhibiting a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by one which is essentially hyperbolic (it has a finite number of transitive hyperbolic attractors with open and dense basin of attraction).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-16T21:35:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "homoclinic bifurcation",
      "dichotomy phenomenon/mechanism",
      "essential hyperbolicity",
      "diffeomorphism",
      "topology c1"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.3836C"
    }
  }
}