{
  "id": "1503.00892",
  "version": "v1",
  "published": "2015-03-03T10:52:03.000Z",
  "updated": "2015-03-03T10:52:03.000Z",
  "title": "On the Ledrappier-Young formula for self-affine measures",
  "authors": [
    "Balázs Bárány"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Ledrappier and Young introduced a relation between entropy, Lyapunov exponents and dimension for invariant measures of diffeomorphisms on compact manifolds. In this paper, we show that a self-affine measure on the plane satisfies the Ledrappier-Young formula if the corresponding iterated function system (IFS) satisfies the strong separation condition and the linear parts satisfy the so called dominated splitting. We give a sufficient condition, inspired by Ledrappier, that the dimensions of such a self-affine measure is equal to the Lyapunov dimension. We show some applications, namely, we give another proof for Hueter-Lalley's classical theorem and we consider self-affine measures and sets generated by lower triangular matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-03T10:52:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C45",
      "28A80"
    ],
    "keywords": [
      "self-affine measure",
      "ledrappier-young formula",
      "strong separation condition",
      "linear parts satisfy",
      "lower triangular matrices"
    ],
    "publication": {
      "doi": "10.1017/S0305004115000419",
      "journal": "Mathematical Proceedings of the Cambridge Philosophical Society",
      "year": 2015,
      "month": "Nov",
      "volume": 159,
      "number": 3,
      "pages": 405
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015MPCPS.159..405B"
    }
  }
}