{
  "id": "1409.5056",
  "version": "v1",
  "published": "2014-09-17T16:26:15.000Z",
  "updated": "2014-09-17T16:26:15.000Z",
  "title": "Complexity and directional entropy in two dimensions",
  "authors": [
    "Ryan Broderick",
    "Van Cyr",
    "Bryna Kra"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the directional entropy of the dynamical system associated to a $\\Z^2$ configuration in a finite alphabet. We show that under local assumptions on the complexity, either every direction has zero topological entropy or some direction is periodic. In particular, we show that all nonexpansive directions in a $\\Z^2$ system with the same local assumptions have zero directional entropy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-17T16:26:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B40",
      "37B10"
    ],
    "keywords": [
      "complexity",
      "dimensions",
      "local assumptions",
      "zero directional entropy",
      "finite alphabet"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.5056B"
    }
  }
}