{
  "id": "2105.12464",
  "version": "v1",
  "published": "2021-05-26T10:42:23.000Z",
  "updated": "2021-05-26T10:42:23.000Z",
  "title": "Higher dimensional topology and generalized Hopf bifurcations for discrete dynamical systems",
  "authors": [
    "Héctor Barge",
    "José M. R. Sanjurjo"
  ],
  "comment": "18 pages, 2 figures",
  "categories": [
    "math.DS",
    "math.GT"
  ],
  "abstract": "In this paper we study generalized Poincar\\'e-Andronov-Hopf bifurcations of discrete dynamical systems. We prove a general result for attractors in n-dimensional manifolds satisfying some suitable conditions. This result allows us to obtain sharper Hopf bifurcation theorems for fixed points in the general case and other attractors in low dimensional manifolds. Topological techniques based on the notion of concentricity of manifolds play a substantial role in the paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-26T10:42:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discrete dynamical systems",
      "higher dimensional topology",
      "generalized hopf bifurcations",
      "sharper hopf bifurcation theorems",
      "study generalized poincare-andronov-hopf bifurcations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}