{
  "abstract": "Let $g$ be a $C^\\infty$ diffeomorphism in the isotopy class of a pseudo-Anosov homeomorphism $f$ such that $g$ and $f$ have the same topological entropy. In 1988, Handel proved that this implies the existence of a semiconjugacy $π$ from $g$ to $f$. He stated that, in general, there is at least one point $x$ such that $π^{-1}(x)$ is disconnected. We show that this is not the case: for every $x$, the set $π^{-1}(x)$ is the intersection of a nested sequence of closed topological disks, and hence is connected. We also prove that there is a unique $g$-invariant probability measure projecting to the measure of maximal entropy of $f$. This measure is entropy-maximizing, hyperbolic, and Bernoulli, and the semiconjugacy induces a metric isomorphism between the corresponding measure-preserving systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03390",
  "author_total": 4,
  "authors": [
    {
      "name": "Pablo D. Carrasco"
    },
    {
      "name": "Federico Rodriguez Hertz"
    },
    {
      "name": "Jana Rodriguez Hertz"
    },
    {
      "name": "Raul Ures"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1reataap1h5kc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03390",
  "fulltext_url": null,
  "id": "1reataap1h5kc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03390",
  "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": "W7208709006",
  "pdf_url": "https://arxiv.org/pdf/2609.03390",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1reataap1h5kc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03390",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03390"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Entropy and semiconjugacy on surfaces",
  "title_text": "Entropy and semiconjugacy on surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/1reataap1h5kc",
  "venue": "arXiv",
  "versions": []
}