{
  "id": "1904.04616",
  "version": "v1",
  "published": "2019-04-09T12:04:33.000Z",
  "updated": "2019-04-09T12:04:33.000Z",
  "title": "Characterization of Separatrices in Holomorphic Dynamical Systems",
  "authors": [
    "Marcus Heitel",
    "Dirk Lebiedz"
  ],
  "comment": "2 pages, 2 figures, extended abstract for conference International Workshop on Model Reduction in Reactive Flows (IWMRRF) in Trondheim in 2019",
  "categories": [
    "math.DS"
  ],
  "abstract": "Multiple time scales in dynamical systems lead to a bundling of trajectories onto slow invariant manifolds (SIMs). Although they are absent in two-dimensional holomorphic dynamical systems, a bundling of orbits is often observed as well. They bundle onto special trajectories called separatrices. We apply numerical methods for the approximation of SIMs to holomorphic flows and show how a separatrix between two regions of periodic orbits can be characterized topologically. Complex time reveals a new perspective on holomorphic dynamical systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-09T12:04:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "separatrix",
      "characterization",
      "slow invariant manifolds",
      "multiple time scales",
      "two-dimensional holomorphic dynamical systems"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 2,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}