{
  "annotation_id": "059e7f1b-7c97-4e35-ab80-8db57a812f68",
  "date_created": "2026-02-17T05:53:11.890000Z",
  "date_modified": "2026-02-17T05:53:11.890000Z",
  "file_hash": "b42b3103029048be6362a0edbb88d47d81f130424a14e8b939651460d22e8816",
  "private": false,
  "record": {
    "abstract": "The dynamics of the left translation semigroup $\\{T_t\\}_{t \\geq 0}$ on weighted $L^p$ spaces over a directed metric tree $L(G)$ is investigated. Necessary and sufficient conditions on the weight family $\\rho$ for the strong continuity of the semigroup are provided. Furthermore, hypercyclicity and weak mixing properties are characterized in terms of the asymptotic decay of $\\rho$ along the tree structure. These results generalize classical $L^p$ translation semigroup dynamics to a graph setting.",
    "arxiv_id": "2601.07561",
    "authors": [
      "Elisabetta Mangino",
      "Alvaro Vargas-Moreno"
    ],
    "categories": [
      "math.FA",
      "math.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Dynamics of the translation semigroup on directed metric trees",
    "url": "https://arxiv.org/abs/2601.07561",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6d787bc2-4464-4c10-8db3-b259da44ae31",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}