{
  "abstract": "Under the framework of time-independent Hamiltonian mechanics on the cotangent bundles $T^*Q$ of the configuration spaces $Q$ of mechanical systems, we introduce the notion of fouling map as a (not necessarily invertible) generalization of the so-called fouling transformations --canonoid transformations preserving configuration coordinates--. We develop a tensorial method for constructing polynomial fouling maps. We show that each such map induces a $(1,1)$-tensor field invariant under the Hamiltonian flow, whose traces of its powers are polynomial constants of motion. For mechanical Hamiltonian functions --the kinetic energy plus the potential energy on a semi-Riemannian configuration space $(Q,g)$--, we completely characterize polynomial bundle maps arising from symmetric $(k+1,0)$-tensor fields and derive the conditions ensuring their fouling nature. Several explicit examples on the Euclidean plane, on the 2-sphere and on a Riemannian manifold with a Liouville metric illustrate the method.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.17407",
  "author_total": 3,
  "authors": [
    {
      "name": "Rafael Azuaje"
    },
    {
      "name": "Juan Carlos Marrero"
    },
    {
      "name": "Edith Padrón"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/drr65k9pvbf4y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.17407",
  "fulltext_url": null,
  "id": "drr65k9pvbf4y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.17407",
  "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.MP"
    ],
    [
      "openalex",
      "2608|Advanced Differential Equations and Dynamical Systems"
    ]
  ],
  "openalex": "W7169860135",
  "pdf_url": "https://arxiv.org/pdf/2607.17407",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/drr65k9pvbf4y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2607.17407",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.17407"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Fouling maps and polynomial first integrals from symmetric tensor fields",
  "title_text": "Fouling maps and polynomial first integrals from symmetric tensor fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/drr65k9pvbf4y",
  "venue": "arXiv",
  "versions": []
}