{
  "id": "1505.01418",
  "version": "v1",
  "published": "2015-05-06T16:16:39.000Z",
  "updated": "2015-05-06T16:16:39.000Z",
  "title": "Convex billiards on convex spheres",
  "authors": [
    "Pengfei Zhang"
  ],
  "comment": "20 pages, 2 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we study the dynamical billiards on a convex 2D sphere. We investigate some generic properties of the convex billiards on a general convex sphere. We prove that $C^\\infty$ generically, every periodic point is either hyperbolic or elliptic with irrational rotation number. Moreover, every hyperbolic periodic point admits some transverse homoclinic intersections. A new ingredient in our approach is that we use Herman's result on Diophantine invariant curves to prove the nonlinear stability of elliptic periodic points for a dense subset of convex billiards.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-06T16:16:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C20",
      "37C29",
      "37D40"
    ],
    "keywords": [
      "convex billiards",
      "hyperbolic periodic point admits",
      "convex 2d sphere",
      "elliptic periodic points",
      "diophantine invariant curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150501418Z"
    }
  }
}