{
  "id": "2212.09881",
  "version": "v1",
  "published": "2022-12-19T22:00:43.000Z",
  "updated": "2022-12-19T22:00:43.000Z",
  "title": "Distribution of Ruelle resonances for real-analytic Anosov diffeomorphisms",
  "authors": [
    "Malo Jézéquel"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove an upper bound for the number of Ruelle resonances for Koopman operators associated to real-analytic Anosov diffeomorphisms: in dimension $d$, the number of resonances larger than $r$ is a $\\mathcal{O}(|\\log r|^d)$ when $r$ goes to $0$. For each connected component of the space of real-analytic Anosov diffeomorphisms on a real-analytic manifold, we prove a dichotomy: either the exponent $d$ in our bound is never optimal, or it is optimal on a dense subset. Using examples constructed by Bandtlow, Just and Slipantschuk, we see that we are always in the latter situation for connected components of the space of real-analytic Anosov diffeomorphisms on the $2$-dimensional torus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-19T22:00:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C30",
      "37D20"
    ],
    "keywords": [
      "real-analytic anosov diffeomorphisms",
      "ruelle resonances",
      "distribution",
      "connected component",
      "dimensional torus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}