{
  "abstract": "For a continuous self-map f of a real interval L, let ent(f) denote the supremum of the topological entropies of the restrictions of f to its compact invariant sets; for a compact interval this is the usual topological entropy. For a class P of maps, the entropy spectrum of P is the set of values ent(f) taken by the maps f in P. We determine the entropy spectra of the three standard classes of chaotic maps of the compact interval [0,1]. Devaney chaotic maps have spectrum [(1/2) log 2, infinity], maps of positive entropy have spectrum (0, infinity], and Li-Yorke chaotic maps have spectrum [0, infinity]; thus every entropy compatible with the known lower bounds actually occurs, and the three spectra are strictly nested. Mixing maps have spectrum ((1/2) log 2, infinity], and Devaney chaotic maps with at least two fixed points have spectrum [log 2, infinity]. As a consequence, a Devaney chaotic map of the interval attains the minimal entropy (1/2) log 2 only if it has a unique fixed point and is not mixing. For an arbitrary interval, compact or not, maps with a point of least period n have spectrum [log sigma_n, infinity], where sigma_n are the Stefan constants, and Li-Yorke chaotic maps have spectrum [0, infinity]. The proofs combine a truncation theorem for maps of non-compact intervals, showing that clipping a map to a compact subinterval never creates entropy; a horseshoe argument showing that two fixed points force entropy log 2 on transitive maps; and explicit constructions, including an exact piecewise linear family, a mixing map of infinite entropy, and a square-root construction that halves the entropy of a transitive map.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39443",
  "author_total": 1,
  "authors": [
    {
      "name": "Vinod Kumar P B"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8jg63502ne023.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39443",
  "fulltext_url": null,
  "id": "8jg63502ne023",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39443",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39443",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8jg63502ne023.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39443",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39443"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "The entropy spectra of chaotic maps of an interval",
  "title_text": "The entropy spectra of chaotic maps of an interval",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/8jg63502ne023",
  "venue": "arXiv",
  "versions": []
}