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Factor-parity Hall sets and controllability — arXiv:2609.04056

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.04056
License (as archived): CC0-1.0
Archived: 2026-10-17T02:26:52.022Z
SHA-256 of the archived text: 0ee438a913ffce91a4e16ce969614c5bedde001c60d7de69cdefd589df4f70f6
Stable URL of this page: https://metraipolis.com/documento/dc_fcab7dfdc6bf

How to cite

Factor-parity Hall sets and controllability — arXiv:2609.04056 — arXiv (en), https://arxiv.org/abs/2609.04056 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_fcab7dfdc6bf (Metraipolis archive dc_fcab7dfdc6bf, sha256 0ee438a913ffce91a4e16ce969614c5bedde001c60d7de69cdefd589df4f70f6)

BibTeX

@misc{dcfcab7dfdc6bf,
  title = {Factor-parity Hall sets and controllability — arXiv:2609.04056},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.04056},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_fcab7dfdc6bf; sha256 0ee438a913ffce91a4e16ce969614c5bedde001c60d7de69cdefd589df4f70f6},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.04056. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-04 in math.OC).
Categorie arXiv: Optimization and Control (math.OC) ; Rings and Algebras (math.RA).
Pagina del lavoro: https://arxiv.org/abs/2609.04056 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T02:07:43.350Z dalla pagina https://arxiv.org/catchup/math.OC/2026-09-04?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).