{
  "id": "1304.4100",
  "version": "v2",
  "published": "2013-04-15T13:52:37.000Z",
  "updated": "2013-11-24T13:01:17.000Z",
  "title": "Some dynamical properties of pseudo-automorphisms in dimension 3",
  "authors": [
    "Tuyen Trung Truong"
  ],
  "comment": "26 pages. Accepted in Transactions of the American Mathematical Society",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "Let $X$ be a compact K\\\"ahler manifold of dimension 3 and let $f:X\\rightarrow X$ be a pseudo-automorphism. Under the mild condition that $\\lambda_1(f)^2>\\lambda_2(f)$, we prove the existence of invariant positive closed $(1,1)$ and $(2,2)$ currents, and we also discuss the (still open) problem of intersection of such currents. We prove a weak equidistribution result (which is essentially known in the literature) for Green $(1,1)$ currents of meromorphic selfmaps, not necessarily 1-algebraic stable, of a compact K\\\"ahler manifold of arbitrary dimension; and discuss how a stronger equidistribution result may be proved for pseudo-automorphisms in dimension 3. As a byproduct, we show that the intersection of some dynamically related currents are well-defined with respect to our definition here, even though not obviously to be seen so using the usual criteria.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-24T13:01:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F99",
      "32H50"
    ],
    "keywords": [
      "dynamical properties",
      "pseudo-automorphism",
      "stronger equidistribution result",
      "weak equidistribution result",
      "mild condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.4100T"
    }
  }
}