{
  "abstract": "Let $\\mathcal F=\\{f_i(x)=r_i x+t_i\\}_{i=0}^{b-1}$ be a self-similar iterated function system (IFS) on $\\mathbb R$ with $b\\ge 3$, and let $K_{\\mathcal F}$ be the associated self-similar set. Given $m\\in\\mathbb N$, for any sequence $ω=ω^0ω^1\\ldots$ with each $ω^i\\in \\{0,1,\\ldots,b-1\\}^m$ a block of length $m$, let \\[ K_{\\mathcal F}^ω:=π_{\\mathcal F}\\left(\\{(d_i)\\in \\{0,1,\\ldots,b-1\\}^{\\mathbb N}: d_{k+1}d_{k+2}\\ldots d_{k+m}\\neω^k\\quad\\forall k\\ge 0\\}\\right), \\] where $π_{\\mathcal F}$ is the natural coding map from $\\{0,1,\\ldots,b-1\\}^{\\mathbb N}$ to $K_{\\mathcal F}$. The set $K_{\\mathcal F}^ω$ is called the survivor set of an open dynamical system with a moving hole related to $ω$. When $\\mathcal F$ is a homogeneous IFS satisfying the open set condition (OSC), the dimensions of $K_{\\mathcal F}^ω$ were determined by the first author, Sun and Wang (Adv. Math., 2026). In this paper we generalize these results to inhomogeneous IFSs. When $\\mathcal F$ satisfies the OSC, we give explicit formulae for the dimensions of $K_{\\mathcal F}^ω$. In particular, we show that the packing dimension and upper box-counting dimension of $K_{\\mathcal F}^ω$ always coincide, while the Hausdorff dimension and lower box-counting dimension of $K_{\\mathcal F}^ω$ are not necessarily equal, which is different from the homogeneous case. Furthermore, when $\\mathcal F$ satisfies the exponential separation condition and the similarity dimension $s_{\\mathcal F}\\le 1$, we are able to determine the Hausdorff dimension of $K_{\\mathcal F}^ω$. Finally, we apply our results to badly approximable numbers and non-recurrence points in the setting of inhomogeneous IFS satisfying the OSC.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31128",
  "author_total": 4,
  "authors": [
    {
      "name": "Derong Kong"
    },
    {
      "name": "Kun Li"
    },
    {
      "name": "Cai-Yun Ma"
    },
    {
      "name": "Károly Simon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9bv4vagrhkkr3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31128",
  "fulltext_url": null,
  "id": "9bv4vagrhkkr3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31128",
  "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.CA"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7223308237",
  "pdf_url": "https://arxiv.org/pdf/2610.31128",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9bv4vagrhkkr3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31128",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31128"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Open dynamics with a moving hole: inhomogeneous IFS and exponential separation condition",
  "title_text": "Open dynamics with a moving hole: inhomogeneous IFS and exponential separation condition",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/9bv4vagrhkkr3",
  "venue": "arXiv",
  "versions": []
}