{
  "abstract": "In the three-rotor problem, three equally massive point particles move on a circle interacting via attractive pairwise cosine potentials. Rotors can represent superconducting phases of metallic segments in a chain of coupled Josephson junctions. We propose a digitization of the classical dynamics that records successive pair and triple coincidences of rotors using four symbols. Rotor coincidences correspond to boundaries in a disjoint partition of the configuration torus into cells where the rotors are ordered clockwise and anticlockwise. It is shown that isolated rotor coincidences must be crossings. Despite being a rather coarse digitization, we find that replacing trajectories by coincidence symbol sequences captures significant qualitative features of the dynamics through word statistics. Word-complexity $C_n$ measures the diversity of $n$-letter words in the symbol sequence while topological entropy governs asymptotic exponential growth of $C_n$. Sequences from periodic orbits have a word-complexity that saturates at the period. Ultra-high-energy trajectories with irrational `slope' are quasiperiodic. We show that they have zero entropy and $C_n = n+3$ by examining limiting slopes and by a mapping to Sturmian sequences. We examine their grammar rules and propose how their right-special words may be identified. On the other hand, numerical investigation of sequences from globally chaotic orbits leads us to conjecture an exponentially growing word-complexity $C_n = 3 \\times 2^{n-1}$ with a topological entropy $\\log 2$. We identify grammar rules that imply this conjectured word-complexity and model the resulting sequences as a subshift of finite type, unlike those at ultra-high energies which are not topological Markov chains.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Chaos 36, 103140 (2026)",
  "arxiv": "2606.25766",
  "author_total": 2,
  "authors": [
    {
      "name": "Govind S. Krishnaswami"
    },
    {
      "name": "Anirudh Rameshan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9fmdfngjxwens.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.25766",
  "fulltext_url": null,
  "id": "9fmdfngjxwens",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.25766",
  "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-ph"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "nlin.CD"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.25766",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9fmdfngjxwens.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:24Z",
      "native_id": "2606.25766",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.25766"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.CD",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Symbol sequences from three-rotor coincidences and their word-complexity",
  "title_text": "Symbol sequences from three-rotor coincidences and their word-complexity",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/9fmdfngjxwens",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1063/5.0354972",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}