{
  "id": "1905.04059",
  "version": "v1",
  "published": "2019-05-10T10:40:40.000Z",
  "updated": "2019-05-10T10:40:40.000Z",
  "title": "Dynamics of the Morse Oscillator: Analytical Expressions for Trajectories, Action-Angle Variables, and Chaotic Dynamics",
  "authors": [
    "Vladimír Krajňák",
    "Stephen Wiggins"
  ],
  "journal": "International Journal of Bifurcation and Chaos, 2019",
  "categories": [
    "math.DS",
    "nlin.CD"
  ],
  "abstract": "We consider the one degree-of-freedom Hamiltonian system defined by the Morse potential energy function (the \"Morse oscillator\"). We use the geometry of the level sets to construct explicit expressions for the trajectories as a function of time, their period for the bounded trajectories, and action-angle variables. We use these trajectories to prove sufficient conditions for chaotic dynamics, in the sense of Smale horseshoes, for the time-periodically perturbed Morse oscillator using a Melnikov type approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-10T10:40:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "morse oscillator",
      "action-angle variables",
      "chaotic dynamics",
      "analytical expressions",
      "trajectories"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}