{
  "id": "1710.01181",
  "version": "v1",
  "published": "2017-10-03T14:21:32.000Z",
  "updated": "2017-10-03T14:21:32.000Z",
  "title": "Quasi-periodic solutions for differential equations with an elliptic-type degenerate equilibrium point under small perturbations",
  "authors": [
    "Xuemei Li",
    "Zaijiu Shang"
  ],
  "comment": "32pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "This work focuses on the existence of quasi-periodic solutions for ordinary and delay differential equations (ODEs and DDEs for short) with an elliptic-type degenerate equilibrium point under quasi-periodic perturbations. We prove that under appropriate hypotheses there exist quasi-periodic solutions for perturbed ODEs and DDEs near the equilibrium point for most parameter values, then apply these results to the delayed van der Pol's oscillator with zero-Hopf singularity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-03T14:21:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic-type degenerate equilibrium point",
      "quasi-periodic solutions",
      "differential equations",
      "small perturbations",
      "delayed van der pols oscillator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}