{
  "id": "2107.01200",
  "version": "v1",
  "published": "2021-07-02T17:42:27.000Z",
  "updated": "2021-07-02T17:42:27.000Z",
  "title": "Genericity of historic behavior for maps and flows",
  "authors": [
    "Maria Carvalho",
    "Paulo Varandas"
  ],
  "comment": "14 pages, revised and improved version of previous preprint \"Minimality and irregular sets\"",
  "categories": [
    "math.DS"
  ],
  "abstract": "We establish a sufficient condition for a continuous map, acting on a compact metric space, to have a Baire residual set of points exhibiting historic behavior (also known as irregular points). This criterion applies, for instance, to a minimal and non-uniquely ergodic map; to maps preserving two distinct probability measures with full support; to non-trivial homoclinic classes; to some non-uniformly expanding maps; and to partially hyperbolic diffeomorphisms with two periodic points whose stable manifolds are dense, including Ma\\~n\\'e and Shub examples of robustly transitive diffeomorphisms. This way, our unifying approach recovers a collection of known deep theorems on the genericity of the irregular set, for both additive and sub-additive potentials, and also provides a number of new applications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-02T17:42:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "genericity",
      "non-trivial homoclinic classes",
      "points exhibiting historic behavior",
      "compact metric space",
      "distinct probability measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}