{
  "id": "1405.2095",
  "version": "v1",
  "published": "2014-05-08T20:48:53.000Z",
  "updated": "2014-05-08T20:48:53.000Z",
  "title": "On intrinsic ergodicity of factors of $\\mathbb{Z}^d$ subshifts",
  "authors": [
    "Kevin McGoff",
    "Ronnie Pavlov"
  ],
  "comment": "22 pages, 6 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "It is well-known that any $\\mathbb{Z}$ subshift with the specification property has the property that every factor is intrinsically ergodic, i.e., every factor has a unique factor of maximal entropy. In recent work, other $\\mathbb{Z}$ subshifts have been shown to possess this property as well, including $\\beta$-shifts and a class of $S$-gap shifts. We give two results that show that the situation for $\\mathbb{Z}^d$ subshifts with $d >1 $ is quite different. First, for any $d>1$, we show that any $\\mathbb{Z}^d$ subshift possessing a certain mixing property must have a factor with positive entropy which is not intrinsically ergodic. In particular, this shows that for $d>1$, $\\mathbb{Z}^d$ subshifts with specification cannot have all factors intrinsically ergodic. We also give an example of a $\\mathbb{Z}^2$ shift of finite type, introduced by Hochman, which is not even topologically mixing, but for which every positive entropy factor is intrinsically ergodic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-08T20:48:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B50"
    ],
    "keywords": [
      "intrinsic ergodicity",
      "specification property",
      "finite type",
      "unique factor",
      "positive entropy factor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.2095M"
    }
  }
}