{
  "abstract": "This paper studies weak mixing for two classes of dynamical systems with the \\(\\mathscr{M}_α\\)-shadowing property using the generic factor characterization of weak scattering. First, for every \\(α\\in[0,1)\\), every \\(M\\)-system with the \\(\\mathscr{M}_α\\)-shadowing property is weakly mixing, thereby answering [P. Oprocha et. al., On partial shadowing of complete pseudo-orbits, J. Math. Anal. Appl., Question~1] negatively. Second, for every \\(α\\in(0,1)\\), the \\(\\mathscr{M}_α\\)-shadowing property implies weak mixing for \\(E\\)-systems and, in particular, for dynamical systems whose measure center is the whole space.Finally, an \\(E\\)-system with the \\(\\mathscr{M}_{0}\\)-shadowing property which is not weakly mixing is constructed, showing that the parameter range \\(α\\in(0,1)\\) in the \\(E\\)-system result is optimal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31724",
  "author_total": 3,
  "authors": [
    {
      "name": "Xinxing Wu"
    },
    {
      "name": "Jidan Wei"
    },
    {
      "name": "Xu Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dvaanqs0md064.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31724",
  "fulltext_url": null,
  "id": "dvaanqs0md064",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31724",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7214777298",
  "pdf_url": "https://arxiv.org/pdf/2609.31724",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dvaanqs0md064.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.31724",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31724"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Weak mixing for dynamical systems with ${\\bm{\\mathscr M}}_{\\bmα}$-shadowing",
  "title_text": "Weak mixing for dynamical systems with ℳ_α-shadowing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/dvaanqs0md064",
  "venue": "arXiv",
  "versions": []
}