{
  "id": "2312.16742",
  "version": "v1",
  "published": "2023-12-27T23:07:42.000Z",
  "updated": "2023-12-27T23:07:42.000Z",
  "title": "Non-uniform hyperbolicity of maps on $\\mathbb{T}^2$",
  "authors": [
    "Sebastián Ramírez",
    "Kendry J. Vivas"
  ],
  "comment": "Comments and suggestions are welcome",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we prove that the homotopy class of non-homothety linear endomorphisms on $\\mathbb{T}^2$ with determinant greater than 2 contains a $C^1$ open set of non-uniformly hyperbolic endomorphisms. Furthermore, we prove that the homotopy class of non-hyperbolic elements (having either $1$ or $-1$ as an eigenvalue) whose degree is large enough contains non-uniformly hyperbolic endomorphisms that are also $C^2$ stably ergodic. These results provide partial answers to certain questions posed in arXiv:2206.08295v2",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-27T23:07:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-uniform hyperbolicity",
      "homotopy class",
      "non-homothety linear endomorphisms",
      "contains non-uniformly hyperbolic endomorphisms",
      "open set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}