{
  "abstract": "Given a dynamical system $(X,T)$ and an ergodic invariant measure $μ$, a $μ$-typical point $x\\in X$ under $T$ visits arbitrarily small neighbourhood of $x$. We will use techniques based on extreme value theory and Laplace functional for point process to show that, for interval maps with suitable mixing and anti-clustering conditions, the limiting distributions of the record times and values of the return process $Y_j(x)=-\\log d(T^jx,x)$, after possible normalisation, has Poisson-type laws.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39928",
  "author_total": 1,
  "authors": [
    {
      "name": "Boyuan Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0ncgrwzcjzm8h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39928",
  "fulltext_url": null,
  "id": "0ncgrwzcjzm8h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39928",
  "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"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39928",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0ncgrwzcjzm8h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39928",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39928"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "On record behaviours of returns for interval maps",
  "title_text": "On record behaviours of returns for interval maps",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/0ncgrwzcjzm8h",
  "venue": "arXiv",
  "versions": []
}