{
  "id": "2302.04641",
  "version": "v1",
  "published": "2023-02-09T13:55:10.000Z",
  "updated": "2023-02-09T13:55:10.000Z",
  "title": "Strange attractors and densely branching trees for the generalized Lozi-like family",
  "authors": [
    "Przemysław Kucharski"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We generalize the Lozi-like family introduced in [M\\v{S}17]. The generalized Lozi-like family encompasses in particular certain Lozi-like maps [M\\v{S}17], orientation preserving or reversing Lozi maps or large parameter regions of 2-dimensional border collision normal forms [GS21]. We prove that it possesses a strange attractor, arising as a homoclinic class. We apply obtained results to extend the Misiurewicz set [Mis80] and its generalization to the orientation preserving case [Kuc22]. We also strengthen results of Paul Glendinning and David Simpson regarding existence of strange attractors for 2-dimensional border collision normal forms [GS22a, GS21]. We also build a model as an inverse limit of densely branching trees for mentioned families, extending results of Jan Boro\\'nski and Sonja \\v{S}timac from [Bor21].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-09T13:55:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D05",
      "37D25",
      "37D45"
    ],
    "keywords": [
      "densely branching trees",
      "strange attractor",
      "generalized lozi-like family",
      "border collision normal forms",
      "large parameter regions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}