{
  "abstract": "We prove quantitative stability and instability estimates for reversible periodic solutions of strictly Legendre-convex Lagrangian systems. If the configuration dimension is $n$, the fixed-period Morse index is $k$, and $k_D,ν_D$ are the Dirichlet index and nullity on a half-period, set \\[ \\widetilde k=k-2k_D-ν_D. \\] Then the algebraic number $ν_+$ of positive real Floquet multipliers satisfies \\[ ν_+\\ge 2n-2\\widetilde k, \\] and we obtain corresponding bounds for the positive real spectrum away from $1$, allowing arbitrary Jordan chains at the unit multiplier. Hence at most $2\\widetilde k$ Floquet multipliers can lie outside the positive real axis. In particular, when $k=0$ we recover the positive-real-spectrum theorem for reversible minimizers, while for nonconstant autonomous brake orbits the bounds improve by two. If, moreover, $n\\ge2$ and the algebraic multiplicity of $1$ is two, an index-one brake orbit is transversely hyperbolic, with $n-1$ stable and $n-1$ unstable directions. Decoupled oscillators show that the refined bounds can be sharp even when the estimate based on $k$ alone is vacuous, and the Hénon--Heiles straight-line orbit provides a nonlinear illustration of the half-period mechanism.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24070",
  "author_total": 2,
  "authors": [
    {
      "name": "Alessandro Portaluri"
    },
    {
      "name": "Li Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/531jk9m093142.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24070",
  "fulltext_url": null,
  "id": "531jk9m093142",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24070",
  "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",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7214011531",
  "pdf_url": "https://arxiv.org/pdf/2609.24070",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/531jk9m093142.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24070",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24070"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Morse Index, Stability and Spectral Bounds for Periodic Orbits in Reversible Lagrangian Systems",
  "title_text": "Morse Index, Stability and Spectral Bounds for Periodic Orbits in Reversible Lagrangian Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/531jk9m093142",
  "venue": "arXiv",
  "versions": []
}