{
  "abstract": "We give a finite-dimensional boundary-residence mechanism for Takens-type historic behavior. For a class of continuous self-maps of a simplex, a multiplicative Lyapunov drift toward the boundary, combined with cyclic residence near separated boundary regions, forces every non-fixed interior orbit to have non-convergent Cesàro averages and non-convergent empirical measures. Thus the historic set has full relative Lebesgue measure. The mechanism is independent of hyperbolic specification, wandering domains and positive entropy: in fact, for the maps considered here the topological entropy is carried entirely by the boundary restriction. The non-convergence persists under all positive powers and, more generally, under multiplicatively thick sampling times. The abstract criterion applies to Stein--Ulam and Lotka--Volterra type stochastic operators once the model-specific cyclic coding and logarithmic residence estimates are verified. In explicit cyclic-collar models we identify the full weak-* accumulation set of empirical measures; this accumulation set is a non-trivial circle of probability measures and yields polynomial pointwise emergence of order \\(\\varepsilon^{-1}\\). We also obtain examples with positive-dimensional omega-limit sets by combining the mechanism with a Barański--Misiurewicz type boundary-tracing construction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18979",
  "author_total": 1,
  "authors": [
    {
      "name": "Farrukh Mukhamedov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/85m6d22ax7hn0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18979",
  "fulltext_url": null,
  "id": "85m6d22ax7hn0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18979",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7213494248",
  "pdf_url": "https://arxiv.org/pdf/2609.18979",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/85m6d22ax7hn0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18979",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18979"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Full-measure historic behavior and emergence in simplex dynamics",
  "title_text": "Full-measure historic behavior and emergence in simplex dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/85m6d22ax7hn0",
  "venue": "arXiv",
  "versions": []
}