{
  "id": "1111.1081",
  "version": "v1",
  "published": "2011-11-04T10:00:24.000Z",
  "updated": "2011-11-04T10:00:24.000Z",
  "title": "Diophantine approximation by orbits of Markov maps",
  "authors": [
    "Lingmin Liao",
    "Stephane Seuret"
  ],
  "comment": "24 pages, 3 figures; To appear in ETDS, 2011",
  "categories": [
    "math.DS",
    "math.CA",
    "math.NT"
  ],
  "abstract": "In 1995, Hill and Velani introduced the shrinking targets theory. Given a dynamical system $([0,1],T)$, they investigated the Hausdorff dimension of sets of points whose orbits are close to some fixed point. In this paper, we study the sets of points well-approximated by orbits $\\{T^n x\\}_{n\\geq 0}$, where $T$ is an expanding Markov map with a finite partition supported by $[0,1]$. The dimensions of these sets are described using the multifractal properties of invariant Gibbs measures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-04T10:00:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K60",
      "28A78"
    ],
    "keywords": [
      "diophantine approximation",
      "invariant gibbs measures",
      "hausdorff dimension",
      "shrinking targets theory",
      "expanding markov map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.1081L"
    }
  }
}