{
  "id": "1311.1184",
  "version": "v3",
  "published": "2013-11-05T20:31:23.000Z",
  "updated": "2014-09-23T18:27:17.000Z",
  "title": "Controlling the stability of periodic orbits of completely integrable systems",
  "authors": [
    "Razvan M. Tudoran"
  ],
  "comment": "19 pages",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "We provide a constructive method designed in order to control the stability of a given periodic orbit of a general completely integrable system. The method consists of a specific type of perturbation, such that the resulting perturbed system becomes a codimension-one dissipative dynamical system which also admits that orbit as a periodic orbit, but whose stability can be a-priori prescribed. The main results are illustrated in the case of a three dimensional dissipative perturbation of the harmonic oscillator, and respectively Euler's equations form the free rigid body dynamics.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-08T13:13:15.000Z",
      "title": "On the stability of periodic orbits of codimension one dissipative dynamical systems",
      "abstract": "We compute explicitly all the characteristic multipliers of a given periodic orbit of a general codimension one dissipative dynamical system. Sufficient conditions to guarantee the partial stability, and respectively the instability of the periodic orbit, are then given. As application of the main results, we propose a method to stabilize with respect to a certain dynamically invariant set, a given periodic orbit of a general completely integrable system. The main results are illustrated in the case of a three dimensional dissipative perturbation of the harmonic oscillator.",
      "comment": "13 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-09-23T18:27:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic orbit",
      "dissipative dynamical system",
      "main results",
      "general codimension",
      "characteristic multipliers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.1184T"
    }
  }
}