{
  "id": "math/0203188",
  "version": "v1",
  "published": "2002-03-19T11:16:42.000Z",
  "updated": "2002-03-19T11:16:42.000Z",
  "title": "Optimal stability and instability results for a class of nearly integrable Hamiltonian systems",
  "authors": [
    "Massimiliano Berti",
    "Luca Biasco",
    "Philippe Bolle"
  ],
  "comment": "6 pages",
  "categories": [
    "math.DS",
    "math.FA"
  ],
  "abstract": "We consider a nearly integrable, non-isochronous, a-priori unstable Hamiltonian system with a (trigonometric polynomial) $O(\\mu)$-perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with diffusion time $T_d = O((1/ \\mu) \\log (1/ \\mu))$ by a variational method which does not require the existence of ``transition chains of tori'' provided by KAM theory. We also prove that our estimate of the diffusion time $T_d$ is optimal as a consequence of a general stability result proved via classical perturbation theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-03-19T11:16:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J40",
      "37J45"
    ],
    "keywords": [
      "integrable hamiltonian systems",
      "optimal stability",
      "instability results",
      "diffusion time",
      "a-priori unstable hamiltonian system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......3188B"
    }
  }
}