{
  "id": "2012.14162",
  "version": "v1",
  "published": "2020-12-28T09:45:36.000Z",
  "updated": "2020-12-28T09:45:36.000Z",
  "title": "α-limit sets and Lyapunov function for maps with one topological attractor",
  "authors": [
    "Ding Yiming",
    "Sun Yun"
  ],
  "comment": "leave blank",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider the topological behaviors of continuous maps with one topological attractor on compact metric space $X$. This kind of map is a generalization of maps such as topologically expansive Lorenz map, unimodal map without homtervals and so on. We provide a leveled $A$-$R$ pair decomposition for such maps, and characterize $\\alpha$-limit set of each point. Based on weak Morse decomposition of $X$, we construct a bounded Lyapunov function $V(x)$, which give a clear description of orbit behavior of each point in $X$ except a meager set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-28T09:45:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B25",
      "37B35",
      "54H20",
      "F.2.2"
    ],
    "keywords": [
      "topological attractor",
      "compact metric space",
      "weak morse decomposition",
      "meager set",
      "bounded lyapunov function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}