{
  "id": "2305.16022",
  "version": "v1",
  "published": "2023-05-25T13:04:22.000Z",
  "updated": "2023-05-25T13:04:22.000Z",
  "title": "Counting periodic orbits on fractals weighted by their Lyapunov exponents",
  "authors": [
    "Ugo Bessi"
  ],
  "comment": "I have omitted a not-so important figure because Arxiv did not accept it",
  "categories": [
    "math.DS"
  ],
  "abstract": "Several authors have shown that Kusuoka's measure $\\kappa$ on fractals is a scalar Gibbs measure; in particular, it maximises a pressure. There is also a different approach, in which one defines a matrix-valued Gibbs measure $\\mu$ which induces both Kusuoka's measure $\\kappa$ and Kusuoka's bilinear form. In the first part of the paper we show that one can define a \"pressure\" for matrix valued measures; this pressure is maximised by $\\mu$. In the second part, we use the matrix-valued Gibbs measure $\\mu$ to count periodic orbits on fractals, weighted by their Lyapounov exponents.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-25T13:04:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "counting periodic orbits",
      "lyapunov exponents",
      "matrix-valued gibbs measure",
      "kusuokas measure",
      "scalar gibbs measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}