{
  "abstract": "We propose the turning-point count-discrepancy indicator (TPCD) for diagnosing orbital chaos from a single trajectory in relativistic Hamiltonian systems with two oscillatory degrees of freedom. TPCD measures the largest cumulative departure of one turning-event count from its mean rate per reference cycle, requiring neither a neighboring orbit nor a phase-space partition and applying to both massive particles and photons. We establish its long-time behavior under explicit event--phase assumptions. Rigid phases with an exact event--phase correspondence obey a strict discrepancy bound of unity, and linearizable regular tori with bounded degree-one phase deformations obey a finite, orbit-dependent bound; both imply that the normalized indicator decays to zero as the record grows. A diffusive fluctuation mechanism instead yields a Brownian-bridge scaling and a finite statistical scale. Integrable Kerr motion validates the construction, recovering prescribed frequency ratios from event counts to within $2.6\\times10^{-5}$ for six targets, including an irrational ratio. In charged-particle scans around a Kerr black hole in an external test magnetic field, TPCD and the fast Lyapunov indicator agree for all 80 sampled trajectories. In the Schwarzschild--Melvin photon model, a trajectory with elevated finite-time TPCD but low fast-Lyapunov values is identified as regular once its indicator trends downward over an extended integration, showing that finite-time values must be read together with their long-time trend.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28914",
  "author_total": 3,
  "authors": [
    {
      "name": "Wenfu Cao"
    },
    {
      "name": "Ying Wang"
    },
    {
      "name": "Hongsheng Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/29t9mmmsmkkz4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28914",
  "fulltext_url": null,
  "id": "29t9mmmsmkkz4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28914",
  "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"
    ],
    [
      "openalex",
      "3109|Quantum chaos and dynamical systems"
    ]
  ],
  "openalex": "W7214339227",
  "pdf_url": "https://arxiv.org/pdf/2609.28914",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/29t9mmmsmkkz4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.28914",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28914"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Turning-Point Count Discrepancy as a Diagnostic of Relativistic Orbital Chaos",
  "title_text": "Turning-Point Count Discrepancy as a Diagnostic of Relativistic Orbital Chaos",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/29t9mmmsmkkz4",
  "venue": "arXiv",
  "versions": []
}