{
  "id": "1509.05246",
  "version": "v1",
  "published": "2015-09-17T13:19:58.000Z",
  "updated": "2015-09-17T13:19:58.000Z",
  "title": "Mean sensitive, mean equicontinuous and almost periodic functions for dynamical systems",
  "authors": [
    "Felipe García-Ramos",
    "Brian Marcus"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We define forms of mean sensitivity for measure theoretical and topological dynamical systems with respect to a given function f. In the measure theoretic case, we show that mean sensitivity with respect to f is complementary to almost periodicity of f, and we obtain a new dynamical characterization of continuous spectrum for Z^d and R^d ergodic systems. In the topological case, we show that a topological version of mean sensitivity with respect to a continuous f is complementary to a topological notion of mean equicontinuity with respect to f. In the hybrid topological/measure-theoretic case, we show that a hybrid notion of mean equicontnuity for f is complementary to the measure-theoretic notion of mean sensitivity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-17T13:19:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "37B10",
      "37B40",
      "37A05",
      "37A30",
      "37A35"
    ],
    "keywords": [
      "dynamical systems",
      "periodic functions",
      "mean sensitivity",
      "mean equicontinuous",
      "mean sensitive"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150905246G"
    }
  }
}