{
  "id": "1510.00723",
  "version": "v1",
  "published": "2015-10-02T20:10:30.000Z",
  "updated": "2015-10-02T20:10:30.000Z",
  "title": "Degree of recurrence of generic diffeomorphisms",
  "authors": [
    "Pierre-Antoine Guihéneuf"
  ],
  "comment": "35 pages. A part of this article is repeted in the annexes of \"Physical measures of discretizations of generic diffeomorphisms\"",
  "categories": [
    "math.DS",
    "cs.DM"
  ],
  "abstract": "We study the spatial discretizations of dynamical systems: can we recover some dynamical features of a system from numerical simulations? Here, we tackle this issue for the simplest algorithm possible: we compute long segments of orbits with a fixed number of digits. We show that the dynamics of the discretizations of a $C^1$ generic conservative diffeomorphism of the torus is very different from that observed in the $C^0$ regularity. The proof of our results involves in particular a local-global formula for discretizations, as well as a study of the corresponding linear case, which uses ideas from the theory of quasicrystals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-02T20:10:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37M05",
      "37A05",
      "37A45",
      "37C20",
      "52C23"
    ],
    "keywords": [
      "generic diffeomorphisms",
      "recurrence",
      "long segments",
      "spatial discretizations",
      "generic conservative diffeomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151000723G"
    }
  }
}