{
  "abstract": "We derive the one-cycle first Magnusian for nonspinning compact binaries on planar, bound eccentric orbits through relative first post-Newtonian (1PN) order and linear order in radiation reaction, and construct the associated first-order periastron return map. Combining the conservative 1PN dynamics and its Jacobi transport with the 2.5PN and 3.5PN radiation-reaction forces, we obtain all four components in closed form for \\(0<e<1\\), without expanding in eccentricity. The dependence on all eight Iyer--Will radiation-reaction gauge parameters reduces to periodic coboundaries and therefore cancels over a radial cycle. The result reproduces the averaged energy and angular-momentum losses, their circular limit, and the secular evolution of the 1PN radial orbital elements. The two remaining components encode the dissipative angle-sector information. Projecting the resulting phase-space update onto the perturbed periastron return section yields the corrections to the return time and apsidal phase. We then compare the strict first-order map with a partially exponentiated map built from the same Magnusian. The comparison is observable dependent: at fixed periastron index, the strict map gives smaller residuals for a representative evolution over 40 radial cycles, whereas partial exponentiation reduces the accumulated periastron-timing residual by about an order of magnitude. Across a representative one-cycle grid at equal masses, partial exponentiation improves the radial-action and energy updates at every sampled point.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01713",
  "author_total": 1,
  "authors": [
    {
      "name": "Andrea Placidi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/831ag7bbk42z1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01713",
  "fulltext_url": null,
  "id": "831ag7bbk42z1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01713",
  "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",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3103|Pulsars and Gravitational Waves Research"
    ]
  ],
  "openalex": "W7207838856",
  "pdf_url": "https://arxiv.org/pdf/2609.01713",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/831ag7bbk42z1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:16Z",
      "native_id": "2609.01713",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01713"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "One-cycle radiation-reaction Magnusian for eccentric binaries through relative 1PN order",
  "title_text": "One-cycle radiation-reaction Magnusian for eccentric binaries through relative 1PN order",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:16Z",
  "url": "https://research.draconitic.com/paper/831ag7bbk42z1",
  "venue": "arXiv",
  "versions": []
}