{
  "id": "2411.17615",
  "version": "v1",
  "published": "2024-11-26T17:27:31.000Z",
  "updated": "2024-11-26T17:27:31.000Z",
  "title": "Minimax approach to optimizations in ergodic theory",
  "authors": [
    "Shoya Motonaga"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We study optimization problems in ergodic theory from the view point of minimax problems. We give minimax characterizations of maximum ergodic averages involving time averages. Our approach works for the abstract variational principle of generalized pressure functions which is proved by Bi\\'{s} et al. (2022). We also describe the relationship between our minimax results and the Fenchel-Rockafellar duality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-26T17:27:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A05",
      "37A50"
    ],
    "keywords": [
      "ergodic theory",
      "minimax approach",
      "study optimization problems",
      "maximum ergodic averages",
      "abstract variational principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}