{
  "id": "1412.5900",
  "version": "v1",
  "published": "2014-12-16T09:49:34.000Z",
  "updated": "2014-12-16T09:49:34.000Z",
  "title": "Spectral properties of renormalization for area-preserving maps",
  "authors": [
    "Denis Gaidashev",
    "Tomas Johnson"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1205.0826",
  "categories": [
    "math.DS"
  ],
  "abstract": "Area-preserving maps have been observed to undergo a universal period-doubling cascade, analogous to the famous Feigenbaum-Coullet-Tresser period doubling cascade in one-dimensional dynamics. A renormalization approach has been used by Eckmann, Koch and Wittwer in a computer-assisted proof of existence of a conservative renormalization fixed point. Furthermore, it has been shown by Gaidashev, Johnson and Martens that infinitely renormalizable maps in a neighborhood of this fixed point admit invariant Cantor sets with vanishing Lyapunov exponents on which dynamics for any two maps is smoothly conjugate. This rigidity is a consequence of an interplay between the decay of geometry and the convergence rate of renormalization towards the fixed point. In this paper we prove a result which is crucial for a demonstration of rigidity: that an upper bound on this convergence rate of renormalizations of infinitely renormalizable maps is sufficiently small.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-16T09:49:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E20",
      "47A75"
    ],
    "keywords": [
      "area-preserving maps",
      "renormalization",
      "spectral properties",
      "feigenbaum-coullet-tresser period doubling cascade",
      "point admit invariant cantor sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.5900G"
    }
  }
}