{
  "abstract": "We introduce a class of Hall sets, which we call factor-parity Hall sets, whose elements split into good and bad brackets. We prove that the good brackets can be steered simultaneously and arbitrarily in small time, which yields sufficient conditions for the small-time local controllability of control-affine systems. This positive result draws on constructions of Kawski, Agrachev-Gamkrelidze and Krastanov. Conversely, we prove that each bad bracket generates an obstruction to controllability, hence a family of necessary conditions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04056",
  "author_total": 2,
  "authors": [
    {
      "name": "Karine Beauchard"
    },
    {
      "name": "Frédéric Marbach"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9aa0mgyzgacfd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04056",
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  "id": "9aa0mgyzgacfd",
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  "language": "en",
  "licence": "CC-BY-SA-4.0",
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  "metadata_licence": "CC0-1.0",
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      "2207|Control and Stability of Dynamical Systems"
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  "pdf_url": "https://hal.science/hal-05769671/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9aa0mgyzgacfd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:43Z",
      "native_id": "hal-05769671",
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      "url": "https://hal.science/hal-05769671v1"
    },
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.04056",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04056"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Factor-parity Hall sets and controllability",
  "title_text": "Factor-parity Hall sets and controllability",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/9aa0mgyzgacfd",
  "venue": "HAL",
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}