{
  "id": "1903.05716",
  "version": "v1",
  "published": "2019-03-13T21:18:30.000Z",
  "updated": "2019-03-13T21:18:30.000Z",
  "title": "Borel subsystems and ergodic universality for compact $\\mathbb Z^d$-systems via specification and beyond",
  "authors": [
    "Nishant Chandgotia",
    "Tom Meyerovitch"
  ],
  "comment": "64 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "A Borel system $(X,S)$ is `almost Borel universal' if any free Borel dynamical system $(Y,T)$ of strictly lower entropy is isomorphic to a Borel subsystem of $(X,S)$, after removing a null set. We obtain and exploit a new sufficient condition for a topological dynamical system to be almost Borel universal. We use our main result to deduce various conclusions and answer a number of questions. Along with additional results, we prove that a `generic' homeomorphism of a compact manifold of topological dimension at least two can model any ergodic transformation, that non-uniform specification implies almost Borel universality, and that $3$-colorings in $\\mathbb Z^d$ and dimers in $\\mathbb Z^2$ are almost Borel universal",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-13T21:18:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A35",
      "37A05",
      "37B50",
      "37B40"
    ],
    "keywords": [
      "borel subsystem",
      "ergodic universality",
      "non-uniform specification implies",
      "free borel dynamical system",
      "sufficient condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 64,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}