{
  "id": "0909.4062",
  "version": "v1",
  "published": "2009-09-22T18:42:35.000Z",
  "updated": "2009-09-22T18:42:35.000Z",
  "title": "Abundance of $C^1$-robust homoclinic tangencies",
  "authors": [
    "C. Bonatti",
    "L. J. Diaz"
  ],
  "comment": "39 pages, 11 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "A diffeomorphism $f$ has a $C^1$-robust homoclinic tangency if there is a $C^1$-neighbourhood $\\cU$ of $f$ such that every diffeomorphism in $g\\in \\cU$ has a hyperbolic set $\\La_g$, depending continuously on $g$, such that the stable and unstable manifolds of $\\La_g$ have some non-transverse intersection. For every manifold of dimension greater than or equal to three, we exhibit a local mechanism (blender-horseshoes) generating diffeomorphisms with $C^1$-robust homoclinic tangencies. Using blender-horseshoes, we prove that homoclinic classes of $C^1$-generic diffeomorphisms containing saddles with different indices and that do not admit dominated splittings (of appropriate dimensions) display $C^1$-robust homoclinic tangencies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-22T18:42:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C05",
      "37C20",
      "37C25",
      "37C29",
      "37C70"
    ],
    "keywords": [
      "robust homoclinic tangency",
      "generic diffeomorphisms containing saddles",
      "appropriate dimensions",
      "dimension greater",
      "hyperbolic set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.4062B"
    }
  }
}