{
  "abstract": "We study the extent to which periodic orbits determine a one-dimensional dynamical system. In particular, we show that they determine every topologically mixing interval map. More generally, for a non-mixing interval map $f$ with dense periodic points, the periodic orbits need not determine $f$, but they always do so for $f^2$. Finally, for maps on compact intervals, we obtain a local version of this rigidity: for each basic set $B$ arising in the spectral decomposition of an interval map $f$, there exists an iterate $f^q$ whose restriction to $B$ is determined by the periodic orbits of $f$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07435",
  "author_total": 3,
  "authors": [
    {
      "name": "Gabriel Fuhrmann"
    },
    {
      "name": "Maik Gröger"
    },
    {
      "name": "Alejandro Passeggi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/67rz919gt5t5v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07435",
  "fulltext_url": null,
  "id": "67rz919gt5t5v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07435",
  "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",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7220938966",
  "pdf_url": "https://arxiv.org/pdf/2610.07435",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/67rz919gt5t5v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07435",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07435"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Period spectrum and rigidity of interval maps",
  "title_text": "Period spectrum and rigidity of interval maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/67rz919gt5t5v",
  "venue": "arXiv",
  "versions": []
}