{
  "abstract": "In this paper, we study typical periodic optimization (TPO) for almost additive potentials in two perturbation spaces. Our main setting is the Banach quotient $\\mathcal E_{\\rm orb}(X,T)$ of orbit-Lipschitz almost additive potentials, where we extend the theory of maximizable sets and countable maximizable families developed by W. Huang, O. Jenkinson, L. Xu and Y. Zhang [Typical periodic optimization for dynamical systems: symbolic dynamics, Invent. Math. 245 (2026), 1--63], and establish a global structural theorem. For a countable maximizable family, global TPO holds if every non boundary member has $X$-extendable TPO and the boundary region has empty interior. As an application, we construct a compact system with global TPO for which $\\mathcal E_{\\rm orb}(X,T)$ is infinite-dimensional and the maximizing periods in open locking regions are unbounded. For a fixed almost additive potential $Φ$, we also develop relative TPO theory on its Lipschitz leaf. When $Φ=0$, this framework reduces to classical Lipschitz TPO. We prove the corresponding leafwise structural theorem and give a non additive rank-one matrix example on a full shift.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29216",
  "author_total": 3,
  "authors": [
    {
      "name": "XiaoYu Zhang"
    },
    {
      "name": "Ercai Chen"
    },
    {
      "name": "Xiaoyao Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9y02vhg74sqez.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29216",
  "fulltext_url": null,
  "id": "9y02vhg74sqez",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29216",
  "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": "W7204890655",
  "pdf_url": "https://arxiv.org/pdf/2608.29216",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9y02vhg74sqez.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29216",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29216"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Maximizing Families and Typical Periodic Optimization for Almost Additive Sequences",
  "title_text": "Maximizing Families and Typical Periodic Optimization for Almost Additive Sequences",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/9y02vhg74sqez",
  "venue": "arXiv",
  "versions": []
}