{
  "id": "2309.01817",
  "version": "v1",
  "published": "2023-09-04T21:10:56.000Z",
  "updated": "2023-09-04T21:10:56.000Z",
  "title": "Invariants and reversibility in polynomial systems of ODEs",
  "authors": [
    "Mateja Grašič",
    "Valery G. Romanovski"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We first investigate the interconnection of invariants of certain group actions and time-reversibility of a class of two-dimensional polynomial systems with $1:-1$ resonant singularity at the origin. The time-reversibility is related to the Sibirsky subvariety of the center (integrability) variety of systems admitting a local analytic first integral near the origin. We propose a new algorithm to obtain a generating set for the Sibirsky ideal of such polynomial systems and investigate some algebraic properties of this ideal. Then, we discuss a generalization of the concept of time-reversibility in the three-dimensional case considering the systems with $1:\\zeta:\\zeta^2$ resonant singularity at the origin (where $\\zeta$ is a primitive cubic root of unity) and study a connection of such reversibility with the invariants of some group actions in the space of parameters of the system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-04T21:10:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34C14"
    ],
    "keywords": [
      "invariants",
      "local analytic first integral",
      "group actions",
      "resonant singularity",
      "time-reversibility"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}