{
  "id": "2001.10647",
  "version": "v1",
  "published": "2020-01-29T00:36:52.000Z",
  "updated": "2020-01-29T00:36:52.000Z",
  "title": "Caustics of weakly Lagrangian distributions",
  "authors": [
    "Sean Gomes",
    "Jared Wunsch"
  ],
  "comment": "27 pages, 3 tables, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study semiclassical sequences of distributions $u_h$ associated to a Lagrangian submanifold of phase space $\\lag \\subset T^*X$. If $u_h$ is a semiclassical Lagrangian distribution, which concentrates at a maximal rate on $\\lag,$ then the asymptotics of $u_h$ are well-understood by work of Arnol'd, provided $\\lag$ projects to $X$ with a stable Lagrangian singularity. We establish sup-norm estimates on $u_h$ under much more general hypotheses on the rate at which it is concentrating on $\\lag$ (again assuming a stable projection). These estimates apply to sequences of eigenfunctions of integrable and KAM Hamiltonians.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-29T00:36:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J40",
      "35A23",
      "58K35"
    ],
    "keywords": [
      "weakly lagrangian distributions",
      "phase space",
      "semiclassical lagrangian distribution",
      "kam hamiltonians",
      "study semiclassical sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}