{
  "id": "0812.0610",
  "version": "v1",
  "published": "2008-12-02T22:31:20.000Z",
  "updated": "2008-12-02T22:31:20.000Z",
  "title": "Simultaneous Continuation of Infinitely Many Sinks Near a Quadratic Homoclinic Tangency",
  "authors": [
    "Eleonora Catsigeras",
    "Marcelo Cerminara",
    "Heber Enrich"
  ],
  "journal": "DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS Volume 29, Number 3, March 2011",
  "doi": "10.3934/dcds.2011.29.693",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that the $C^3$ diffeomorphisms on surfaces, exhibiting infinitely many sinksnear the generic unfolding of a quadratic homoclinic tangency of a dissipative saddle, can be perturbed along an infinite dimensional manifold of $C^3$ diffeomorphisms such that infinitely many sinks persist simultaneously. On the other hand, if they are perturbed along one-parameter families that unfold generically the quadratic tangencies, then at most a finite number of those sinks have continuation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-12-02T22:31:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37G35",
      "37D05"
    ],
    "keywords": [
      "quadratic homoclinic tangency",
      "simultaneous continuation",
      "infinite dimensional manifold",
      "diffeomorphisms"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.0610C"
    }
  }
}