{
  "id": "2112.00051",
  "version": "v2",
  "published": "2021-11-30T19:17:33.000Z",
  "updated": "2022-08-03T16:46:04.000Z",
  "title": "Some Generic Properties of Partially Hyperbolic Endomorphisms",
  "authors": [
    "F. Micena",
    "J. S. C. Costa"
  ],
  "comment": "16 pages, two pictures. Submitted for publication in Nonlinearity. This is a more organized version with implemented suggestions by the referees",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this work, we deal with a notion of partially hyperbolic endomorphism. We explore topological properties of this definition and we obtain, among other results, obstructions to get center leaf conjugacy with the linear part, for a class of partially hyperbolic endomorphism $C^1-$sufficiently close to a hyperbolic linear endomorphism. Indeed such obstructions are related to the number of center directions of a point. We provide examples illustrating these obstructions. We show that for a manifold $M$ with dimension $n \\geq 3,$ admitting a non-invertible partially hyperbolic endomorphisms, there is a $C^1$ open and dense subset $\\mathcal{U}$ of all partially hyperbolic endomorphisms with degree $d \\geq n,$ such that any $f \\in \\mathcal{U}$ is neither $c$ nor $u$ special.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-08-03T16:46:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generic properties",
      "hyperbolic linear endomorphism",
      "obstructions",
      "center leaf conjugacy",
      "center directions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}