{
  "id": "2208.06491",
  "version": "v1",
  "published": "2022-08-12T20:33:37.000Z",
  "updated": "2022-08-12T20:33:37.000Z",
  "title": "Solution manifolds of differential systems with discrete state-dependent delays are almost graphs",
  "authors": [
    "Tibor Krisztin",
    "Hans-Otto Walther"
  ],
  "comment": "16 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that for a system $$ x'(t)=g(x(t-d_1(Lx_t)),\\dots,x(t-d_k(Lx_t))) $$ of $n$ differential equations with $k$ discrete state-dependent delays the solution manifold, on which solution operators are differentiable, is nearly as simple as a graph over a closed subspace in $C^1([-r,0],\\mathbb{R}^n)$. The map $L$ is continuous and linear from $C([-r,0],\\mathbb{R}^n)$ onto a finite-dimensional vectorspace, and $g$ as well as the delay functions $d_{\\kappa}$ are assumed to be continuously differentiable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-12T20:33:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34K43",
      "34K19",
      "34K05",
      "58D25"
    ],
    "keywords": [
      "discrete state-dependent delays",
      "solution manifold",
      "differential systems",
      "delay functions",
      "solution operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}