{
  "id": "2206.14878",
  "version": "v1",
  "published": "2022-06-29T19:44:40.000Z",
  "updated": "2022-06-29T19:44:40.000Z",
  "title": "Arnold diffusion in a model of dissipative system",
  "authors": [
    "Samuel W. Akingbade",
    "Marian Gidea",
    "Tere M-Seara"
  ],
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP",
    "nlin.CD"
  ],
  "abstract": "We consider a mechanical system consisting of a rotator and a pendulum coupled via a small, time-periodic Hamiltonian perturbation. The Arnold diffusion problem asserts the existence of `diffusing orbits' along which the energy of the rotator grows by an amount independent of the size of the coupling parameter, for all sufficiently small values of the coupling parameter. There is a vast literature on establishing Arnold diffusion for such systems. In this work, we consider the case when an additional, damping perturbation is added to the system. The resulting system has energy dissipation. We provide explicit conditions on the damping parameter, so that the resulting dissipative system still exhibits diffusing orbits. The fact that Arnold diffusion may play a role in systems with small dissipation was conjectured by Chirikov. In this work, the coupling is carefully chosen, however we plan to consider general couplings in future work.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-29T19:44:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dissipative system",
      "arnold diffusion problem asserts",
      "coupling parameter",
      "diffusing orbits",
      "time-periodic hamiltonian perturbation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}