{
  "id": "2405.11434",
  "version": "v1",
  "published": "2024-05-19T03:42:37.000Z",
  "updated": "2024-05-19T03:42:37.000Z",
  "title": "Generic behavior of differentially positive systems on a globally orderable Riemannian manifold",
  "authors": [
    "Lin Niu",
    "Yi Wang"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Differentially positive systems are the nonlinear systems whose linearization along trajectories preserves a cone field on a smooth Riemannian manifold. One of the embryonic forms for cone fields in reality is originated from the general relativity. By utilizing the Perron-Frobenius vector fields and the $\\Gamma$-invariance of cone fields, we show that generic (i.e.,``almost all\" in the topological sense) orbits are convergent to certain single equilibrium. This solved a reduced version of Forni-Sepulchre's conjecture in 2016 for globally orderable manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-19T03:42:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "globally orderable riemannian manifold",
      "differentially positive systems",
      "generic behavior",
      "cone field",
      "smooth riemannian manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}