{
  "abstract": "Let $a,b$ be multiplicatively independent integers. We prove that if $μ$ is a zero-entropy non-atomic $\\times a$-invariant measure on $[0,1]$, then $μ$-a.e.~$x$ has dense $\\times b$-orbit. Related statements follow for many closed $\\times a$-invariant sets, and in particular we conclude the existence of irrational numbers with minimal complexity in base $a$ and maximal complexity in base $b$. We extend~these results to commuting endomorphisms of the torus under an irreducibility and hyperbolicity condition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21481",
  "author_total": 1,
  "authors": [
    {
      "name": "Michael Hochman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/er0q9pctxtak3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21481",
  "fulltext_url": null,
  "id": "er0q9pctxtak3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21481",
  "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": "W7213933773",
  "pdf_url": "https://arxiv.org/pdf/2609.21481",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/er0q9pctxtak3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21481",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21481"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Dense times-b orbits from times-a invariant sets and measures, in zero entropy",
  "title_text": "Dense times-b orbits from times-a invariant sets and measures, in zero entropy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/er0q9pctxtak3",
  "venue": "arXiv",
  "versions": []
}