{
  "abstract": "We present a systematic approach to characterize Devaney chaos in the solution of homogeneous one dimensional constant-coefficients PDEs on Herzog spaces. We show that for equations where the highest-order time derivative lacks mixed spatial derivatives, there always exists a weighted space in which the solution is chaotic. This analysis is extended to include mixed partial derivatives in the highest-order temporal term. Moreover, we link the chaotic behavior in Herzog spaces to the semidiscretization of the equations by identifying isometric isomorphisms between the two contexts, providing also a characterization for chaos on these semidiscretizations. The work concludes with two applications that provide new insights on the dynamics of the fourth-order Moore-Gibson-Thompson equation and the viscous van Wijngaarden-Eringen equation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31126",
  "author_total": 1,
  "authors": [
    {
      "name": "Álvaro Vargas-Moreno"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/706vjkj1w2q4d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31126",
  "fulltext_url": null,
  "id": "706vjkj1w2q4d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31126",
  "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.DS"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7214647830",
  "pdf_url": "https://arxiv.org/pdf/2609.31126",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/706vjkj1w2q4d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.31126",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31126"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "A Systematic Approach to Chaos In PDEs and their Semidiscretizations",
  "title_text": "A Systematic Approach to Chaos In PDEs and their Semidiscretizations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/706vjkj1w2q4d",
  "venue": "arXiv",
  "versions": []
}