{
  "id": "2010.15291",
  "version": "v1",
  "published": "2020-10-29T00:34:57.000Z",
  "updated": "2020-10-29T00:34:57.000Z",
  "title": "Dynamical characterization of initial segments of the Markov and Lagrange spectra",
  "authors": [
    "Davi Lima",
    "Carlos Gustavo Moreira"
  ],
  "comment": "24 pages",
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "We prove that, for every $k\\ge 4$, the sets $M(k)$ and $L(k)$, which are Markov and Lagrange dynamical spectra related to conservative horseshoes and associated to continued fractions with coefficients bounded by $k$ coincide with the intersections of the classical Markov and Lagrange spectra with $(-\\infty, \\sqrt{k^2+4k}]$. We also observe that, despite the corresponding statement is also true for $k = 2$, it is false for $k = 3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-29T00:34:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lagrange spectra",
      "initial segments",
      "dynamical characterization",
      "lagrange dynamical spectra",
      "horseshoes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}