{
  "id": "2010.11337",
  "version": "v1",
  "published": "2020-10-21T22:37:39.000Z",
  "updated": "2020-10-21T22:37:39.000Z",
  "title": "Ergodic decompositions of Burger-Roblin measures on Anosov homogeneous spaces",
  "authors": [
    "Minju Lee",
    "Hee Oh"
  ],
  "comment": "24 pages",
  "categories": [
    "math.DS",
    "math.GT"
  ],
  "abstract": "Let $G$ be a connected semisimple real algebraic group and $\\Gamma$ a Zariski dense Anosov subgroup of $G$. Let $N$ be a maximal horospherical subgroup of $G$ and $P$ its normalizer with a fixed Langlands decomposition $P=MAN$. We show that each $N$-invariant Burger-Roblin measure on $\\Gamma\\backslash G$ decomposes into at most $[M:M^\\circ]$-number of $N$-ergodic components, and deduce the following refinement of the main result of the previous paper by the authors: the space of all non-trivial $N$-invariant ergodic and $M^\\circ A$-quasi-invariant Radon measures on $\\Gamma\\backslash G$, modulo the translations by $M$, is homeomorphic to ${\\mathbb R}^{\\text{rank }G-1}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-21T22:37:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "anosov homogeneous spaces",
      "ergodic decompositions",
      "connected semisimple real algebraic group",
      "zariski dense anosov subgroup",
      "invariant burger-roblin measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}