{
  "id": "1711.05543",
  "version": "v1",
  "published": "2017-11-15T12:47:46.000Z",
  "updated": "2017-11-15T12:47:46.000Z",
  "title": "Time-Changes of Heisenberg nilflows",
  "authors": [
    "Giovanni Forni",
    "Adam Kanigowski"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider the three dimensional Heisenberg nilflows. Under a full measure set Diophantine condition on the generator of the flow we construct Bufetov functionals which are asymptotic to ergodic integrals for sufficiently smooth functions, have a modular property and scale exactly under the renor- malization dynamics. We then prove analyticity of the functionals in the transverse directions to the flow. As a consequence of this analyticity property we derive that there exists a full measure set of nilflows such that generic (non-trivial) time-changes are mixing and moreover have a \"stretched polynomial\" decay of correlations for sufficiently smooth functions. Moreover we also prove that there exists a full Hausdorff dimension set of nilflows such that generic non-trivial time-changes have polynomial decay of correlations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-15T12:47:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "time-changes",
      "sufficiently smooth functions",
      "full measure set diophantine condition",
      "full hausdorff dimension set",
      "construct bufetov functionals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}