{
  "id": "2505.09575",
  "version": "v1",
  "published": "2025-05-14T17:26:08.000Z",
  "updated": "2025-05-14T17:26:08.000Z",
  "title": "Conjugacies of Expanding Skew Products on $\\mathbb{T}^n$",
  "authors": [
    "Gregory Hemenway"
  ],
  "comment": "14 pages, 4 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that any equilibrium state for a H\\\"older potential on the model map $\\vec{x} \\mapsto d \\cdot \\vec{x} \\mod \\mathbb{Z}^n$ on $\\mathbb{T}^n$ is conjugate to Lebesgue measure for an invariant expanding skew product of degree $d$. This is a generalization of a result of McMullen to higher dimensions for equilibrium states. We use an approach developed by the author using a family of nonstationary transfer operators for an expanding skew product. We also apply a Markov partition argument to classify invariant probability measures for expanding maps on $\\mathbb{T}^n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-14T17:26:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D35",
      "37C30"
    ],
    "keywords": [
      "equilibrium state",
      "conjugacies",
      "invariant expanding skew product",
      "nonstationary transfer operators",
      "markov partition argument"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}