{
  "abstract": "We study linearizations of dynamical systems and some of its topological properties. Special attention is paid to the case of Lipschitz-free operators, and they are shown to model the dynamics of very general linearizations. We provide a new criterion, called the targeting property, for the (weakly) mixing property in a linear dynamical system through a (possibly) non-linear restriction of it. We then apply this criterion to the linearization $T_f$ of a Lipschitz map $f\\colon M\\to M$, where $M$ is a metric space and the operator $T_f$ is defined on the corresponding Lipschitz-free space $\\mathcal F (M)$---the so-called Lipschitz-free operators. We show that, under some natural assumptions on the distance considered in $M$, the operator $T_f$ is hypercyclic if and only if the map $f$ has the targeting property.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17874",
  "author_total": 4,
  "authors": [
    {
      "name": "Christian Cobollo"
    },
    {
      "name": "Romuald Ernst"
    },
    {
      "name": "Quentin Menet"
    },
    {
      "name": "Alfred Peris"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9acyb7psnvhvh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17874",
  "fulltext_url": null,
  "id": "9acyb7psnvhvh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17874",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7213503007",
  "pdf_url": "https://arxiv.org/pdf/2609.17874",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9acyb7psnvhvh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.17874",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17874"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Hypercyclicity and Lipschitz-free operators",
  "title_text": "Hypercyclicity and Lipschitz-free operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/9acyb7psnvhvh",
  "venue": "arXiv",
  "versions": []
}