{
  "id": "2307.03815",
  "version": "v1",
  "published": "2023-07-07T20:05:35.000Z",
  "updated": "2023-07-07T20:05:35.000Z",
  "title": "Dynamical Systems: Discrete, Continuous and Hybrid",
  "authors": [
    "Ethan Akin"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "The dynamics by iteration of a function on a compact metric space, sometimes called a cascade, can be extended to the dynamics of a closed relation on such a space. Here we apply this relation dynamics to study semiflows (and their relation extension) as well as hybrid dynamical systems which combine both continuous time and discrete time dynamics. In a unified way we describe the attractor-repeller structure, Conley's chain recurrence relation and the construction of Lyapunov functions for all of these systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-07T20:05:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B20",
      "37B25",
      "37B39",
      "37C70"
    ],
    "keywords": [
      "conleys chain recurrence relation",
      "continuous",
      "compact metric space",
      "discrete time dynamics",
      "lyapunov functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}