{
  "abstract": "Let $X$ be a separable locally compact metric space, let $E\\neq\\{0\\}$ be a normed space, and let $G$ be a semigroup of continuous self-maps of $X$. Every $φ\\in G$ induces the composition operator $C_φf=f\\circφ$ on the space $C(X,E)$ of continuous functions endowed with the compact-open topology. We characterize the topological transitivity of the semigroup $\\widehat{G}=\\{C_φ:φ\\in G\\}$ by a condition that combines the run-away property of $G$ with an approximate form of injectivity, and we show that, when $E$ is separable, $\\widehat{G}$ is topologically transitive if and only if it is hypercyclic. In particular, if every element of $G$ is one-to-one and $G$ is run-away, then $\\widehat{G}$ is topologically transitive, and hypercyclic when $E$ is separable. For a single map $φ$ we obtain: $C_φ$ is hypercyclic $\\iff$ $C_φ$ is topologically transitive $\\iff$ $φ$ is one-to-one and run-away, and $C_φ$ is mixing $\\iff$ $φ$ is one-to-one and strongly run-away. If, moreover, $φ$ is an open map (which is automatic on manifolds by invariance of domain), then $C_φ$ is Devaney chaotic. On an open interval all of these properties are equivalent to $φ$ being one-to-one without fixed points.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: M. Javaheri, Hypercyclic and topologically transitive semigroups of composition operators, Topology Appl. 164 (2014), 105--112",
  "arxiv": "2611.08320",
  "author_total": 1,
  "authors": [
    {
      "name": "Mohammad Javaheri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/crs09brzjeabb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08320",
  "fulltext_url": null,
  "id": "crs09brzjeabb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08320",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08320",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/crs09brzjeabb.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.08320",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08320"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Hypercyclic and topologically transitive semigroups of composition operators (revised and extended version)",
  "title_text": "Hypercyclic and topologically transitive semigroups of composition operators (revised and extended version)",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:49Z",
  "url": "https://research.draconitic.com/paper/crs09brzjeabb",
  "venue": "arXiv",
  "versions": []
}