{
  "id": "math/0302181",
  "version": "v1",
  "published": "2003-02-15T17:18:19.000Z",
  "updated": "2003-02-15T17:18:19.000Z",
  "title": "On projections onto odometers of dynamical systems with the compact phase space",
  "authors": [
    "Eugene Polulyakh"
  ],
  "comment": "62 pages in LaTeX 2-e",
  "categories": [
    "math.DS"
  ],
  "abstract": "We investigate projections to odometers (group rotations over adic groups) of topological invertible dynamical systems with discrete time and compact Hausdorff phase space. For a dynamical system $(X, f)$ with a compact phase space we consider the category of its projections onto odometers. We examine the connected partial order relation on the class of all objects of a skeleton of this category. We claim that this partially ordered class always have maximal elements and characterize them. It is claimed also, that this class have a greatest element and is isomorphic to some characteristic for the dynamical system $(X, f)$ subset of the set $\\Sigma$ of ultranatural numbers if and only if the dynamical system $(X, f)$ is indecomposable (the space $X$ could not be decomposed into two proper disjoint closed invariant subsets).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-02-15T17:18:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "37B20"
    ],
    "keywords": [
      "dynamical system",
      "compact phase space",
      "projections",
      "proper disjoint closed invariant subsets",
      "compact hausdorff phase space"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 62,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......2181P"
    }
  }
}