{
  "abstract": "We consider the FPUT $α$-model with $N$ particles and initial data with small total energy $E$, independent of $N$. In particular, we prove that if the energy is initially given to Fourier modes of wave number $πk/N\\leq θ_*$, then it does not flow to modes of wave number larger than $θ_*$ up to long times of order $E^{-(1-ε/2)}$, $θ_*$ and $ε$ being small numbers. The proof relies on the closeness of the Toda lattice to the FPUT system. Unlike previous approaches, we do not make use of the action-angle variables of the Toda system, but we exploit the Flaschka integrals of the latter. Actually, we find a suitable recombination of the Flaschka integrals whose quadratic part is used to control the packet, the higher order part fulfilling very good estimates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23119",
  "author_total": 2,
  "authors": [
    {
      "name": "Dario Bambusi"
    },
    {
      "name": "Antonio Ponno"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9hzpv52htwz3a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23119",
  "fulltext_url": null,
  "id": "9hzpv52htwz3a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23119",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7213998266",
  "pdf_url": "https://arxiv.org/pdf/2609.23119",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9hzpv52htwz3a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.23119",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23119"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Long time stability of low--frequency packets of modes at finite total energy",
  "title_text": "Long time stability of low--frequency packets of modes at finite total energy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/9hzpv52htwz3a",
  "venue": "arXiv",
  "versions": []
}