{
  "id": "2209.13245",
  "version": "v1",
  "published": "2022-09-27T08:34:35.000Z",
  "updated": "2022-09-27T08:34:35.000Z",
  "title": "A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class",
  "authors": [
    "Christian Bonatti",
    "Katsutoshi Shinohara"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We give a $C^1$-perturbation technique for ejecting an a priori given finite set of periodic points preserving a given finite set of homo/hetero-clinic intersections from a chain recurrence class of a periodic point. The technique is first stated under a simpler setting called Markov iterated function system, a two dimensional iterated function system in which the compositions are chosen in Markovian way. Then we apply the result to the setting of three dimensional partially hyperbolic diffeomorphisms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-27T08:34:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B25",
      "37D30",
      "37G35"
    ],
    "keywords": [
      "partially hyperbolic chain recurrence class",
      "finite set",
      "periodic point",
      "dimensional iterated function system",
      "markov iterated function system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}