{
  "abstract": "Our previous work [Y.~Li, D.~Xu, and Y.~Hao, Phys. Rev. Accel. Beams \\textbf{28}, 074001 (2025)] introduced a square-matrix method for constructing approximate invariants recursively, order by order, from the one-turn map of non-integrable Hamiltonian systems. At fourth and higher even orders, the recursive construction is intrinsically non-unique because rotationally invariant polynomials generate a null space in the corresponding homological equations. In the resonant regime, this ambiguity can lead to an incorrect description of the resonance-island topology and is therefore particularly relevant to accelerator applications that rely on stable resonance islands. In this work, we select the null-space contributions by explicitly incorporating the null-space basis vectors and determining their coefficients through an averaging procedure over a prescribed region of interest. The method is demonstrated using the Kobayashi map near a third-order resonance, extending the square-matrix construction to resonant Hamiltonian dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06462",
  "author_total": 4,
  "authors": [
    {
      "name": "Yongjun Li"
    },
    {
      "name": "Derong Xu"
    },
    {
      "name": "Yue Hao"
    },
    {
      "name": "Sergei Nagaitsev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eszct7183pg17.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06462",
  "fulltext_url": null,
  "id": "eszct7183pg17",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06462",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.acc-ph"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7220660906",
  "pdf_url": "https://arxiv.org/pdf/2610.06462",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eszct7183pg17.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.06462",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06462"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.acc-ph",
      "subfield": "applied-instrumentation"
    }
  ],
  "title": "Construction of Approximate Invariants Across Nonlinear Resonances",
  "title_text": "Construction of Approximate Invariants Across Nonlinear Resonances",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/eszct7183pg17",
  "venue": "arXiv",
  "versions": []
}