{
  "annotation_id": "bf5c0421-cc8d-4db6-abde-5e5532c5ab15",
  "date_created": "2026-03-02T18:02:51.349000Z",
  "date_modified": "2026-03-02T18:02:51.349000Z",
  "file_hash": "e79b98afc1034d04429234b6c563698f2b5c2d5adf6573ef1e2e2a73dffc417f",
  "private": false,
  "record": {
    "abstract": "The investigation of nonlinear dynamical systems of the type\n$\\dot{x}=P(x,y,z),\\dot{y}=Q(x,y,z),\\dot{z}=R(x,y,z)$ by means of reduction to\nsome ordinary differential equations of the second order in the form\n$y\u0027\u0027+a_1(x,y)y\u0027^3+3a_2(x,y)y\u0027^2+3a_3(x,y)y\u0027+a_4(x,y)=0$ is done. The main\nbackbone of this investigation was provided by the theory of invariants\ndeveloped by S. Lie, R. Liouville and A. Tresse at the end of the 19th century\nand the projective geometry of E. Cartan. In our work two, in some sense\nsupplementary, systems are considered: the Lorenz system $\\dot{x}=\\sigma (y-x),\n\\dot{y}=rx-y-zx,\\dot{z}=xy-bz $ and the R\\\"o\\ss ler system\n$\\dot{x}=-y-z,\\dot{y}=x+ay,\\dot{z}=b+xz-cz.$. The invarinats for the ordinary\ndifferential equations, which correspond to the systems mentioned abouve, are\nevaluated. The connection of values of the invariants with characteristics of\ndynamical systems is established.",
    "arxiv_id": "solv-int/9705006",
    "authors": [
      "L. A. Bordag",
      "V. S. Dryuma"
    ],
    "categories": [
      "solv-int",
      "chao-dyn",
      "nlin.CD",
      "nlin.SI"
    ],
    "doi": "10.1007/s000330050061",
    "title": "Investigation of dynamical systems using tools of the theory of   invariants and projective geometry",
    "url": "https://arxiv.org/abs/solv-int/9705006"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2a956fb9-dc0f-4e9c-b3c9-67dfa48dfe3f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}