{
  "abstract": "We consider the direct product of two symplectomorphisms, one of which exhibits a basic set and the other one a non-degenerate elliptic equilibrium. Under a local domination condition we show that a typical real-analytic deformations of this system display large robustly transitive sets. As a corollary of our construction we also obtain new open sets of real-analytic symplectomorphisms which are topologically mixing but not uniformly hyperbolic. To establish these results we develop perturbation techniques to create blender horseshoes in the real-analytic setting and import ideas from control theory which show that, typically, these objects have a large domain of influence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.15922",
  "author_total": 1,
  "authors": [
    {
      "name": "Jaime Paradela"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7nf9wz2h2xxnr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.15922",
  "fulltext_url": null,
  "id": "7nf9wz2h2xxnr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.15922",
  "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": "W7161578633",
  "pdf_url": "https://arxiv.org/pdf/2605.15922",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7nf9wz2h2xxnr.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:09Z",
      "native_id": "2605.15922",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.15922"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Robustly transitive behavior in symplectic dynamics",
  "title_text": "Robustly transitive behavior in symplectic dynamics",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:21Z",
  "url": "https://research.draconitic.com/paper/7nf9wz2h2xxnr",
  "venue": "arXiv",
  "versions": []
}