{
  "abstract": "We develop a method for constructing minimal subshifts with a prescribed bound on the factor complexity within any strong orbit equivalence (SOE) class. This implies realizations of topological entropies within any SOE class, strengthening a series of classical results by Sugisaki. While prior work established complexity controls for zero-entropy systems, the approach of the present work extends to positive-entropy regimes. Our construction introduces the class of pseudo-Toeplitz subshifts, and we show that they exist in any SOE class. More precisely, for any $α\\geq 1$ and sequence $g_n$ growing exponentially at rate $\\log(α)$, we construct a system in this class whose topological entropy is $\\log(α)$ and whose complexity grows strictly faster, or, under certain conditions, slower than $g_n$. As a consequence, any Choquet simplex can be realized as the set of invariant measures of a Toeplitz subshift with precisely controlled complexity, in either a zero or positive-entropy regime.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27313",
  "author_total": 2,
  "authors": [
    {
      "name": "Paulina Cecchi-Bernales"
    },
    {
      "name": "Sebastián Donoso"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/61ja6960tt465.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27313",
  "fulltext_url": null,
  "id": "61ja6960tt465",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27313",
  "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": "W7214153231",
  "pdf_url": "https://arxiv.org/pdf/2609.27313",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/61ja6960tt465.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27313",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27313"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Entropy and complexity in a strong orbit equivalence class via pseudo-Toeplitz subshifts",
  "title_text": "Entropy and complexity in a strong orbit equivalence class via pseudo-Toeplitz subshifts",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/61ja6960tt465",
  "venue": "arXiv",
  "versions": []
}