{
  "id": "1101.2521",
  "version": "v1",
  "published": "2011-01-13T09:50:57.000Z",
  "updated": "2011-01-13T09:50:57.000Z",
  "title": "Existence of orbits with non-zero torsion for certain types of surface diffeomorphisms",
  "authors": [
    "François Béguin",
    "Zouhour Rezig Boubaker"
  ],
  "comment": "3 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "The present paper concerns the dynamics of surface diffeomorphisms. Given a diffeomorphism $f$ of a surface $S$, the \\emph{torsion} of the orbit of a point $z\\in S$ is, roughly speaking, the average speed of rotation of the tangent vectors under the action of the derivative of $f$, along the orbit of $z$ under $f$. The purpose of the paper is to identify some situations where there exist measures and orbits with non-zero torsion. We prove that every area preserving diffeomorphism of the disc which coincides with the identity near the boundary has an orbit with non-zero torsion. We also prove that a diffeomorphism of the torus $\\mathbb{T}^2$, isotopic to the identity, whose rotation set has non-empty interior, has an orbit with non-zero torsion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-01-13T09:50:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E30",
      "37E45"
    ],
    "keywords": [
      "non-zero torsion",
      "surface diffeomorphisms",
      "paper concerns",
      "tangent vectors",
      "area preserving diffeomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.2521B"
    }
  }
}