{
  "id": "2411.08571",
  "version": "v2",
  "published": "2024-11-13T12:33:15.000Z",
  "updated": "2025-01-30T16:37:06.000Z",
  "title": "Essential dynamics in chaotic attractors",
  "authors": [
    "Eran Igra"
  ],
  "categories": [
    "math.DS",
    "math.CA"
  ],
  "abstract": "We prove that if a smooth vector field $F$ of $S^3$ generates a sufficiently complicated heteroclinic knot, the flow also generates infinitely many periodic orbits, which persist under smooth perturbations which preserve the heteroclinic knot. Consequentially, we then associate a Template with the flow dynamics - regardless of whether $F$ satisfies any hyperbolicity condition or not. In addition, inspired by the Thurston-Nielsen Classification Theorem, we also conclude topological criteria for the existence of chaotic dynamics for three-dimensional flows - which we apply to study both the R\\\"ossler and Lorenz attractors.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-01-30T16:37:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C10",
      "37C27",
      "37C29",
      "37C70",
      "37B99",
      "37G35"
    ],
    "keywords": [
      "chaotic attractors",
      "essential dynamics",
      "smooth vector field",
      "thurston-nielsen classification theorem",
      "chaotic dynamics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}