{
  "id": "2404.00078",
  "version": "v1",
  "published": "2024-03-29T03:55:50.000Z",
  "updated": "2024-03-29T03:55:50.000Z",
  "title": "Irreversible and dissipative systems",
  "authors": [
    "J. Beck",
    "W. W. L. Chen",
    "Y. Yang"
  ],
  "comment": "42 pages, 38 figures",
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "We study some new dynamical systems where the corresponding piecewise linear flow is neither time reversible nor measure preserving. We create a dissipative system by starting with a finite polysquare translation surface, and then modifying it by including a one-sided barrier on a common vertical edge of two adjacent atomic squares, in the form of a union of finitely many intervals. The line flow in this system partitions the system into a transient set and a recurrent set. We are interested in the geometry of these two sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-29T03:55:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E35",
      "11K38"
    ],
    "keywords": [
      "dissipative system",
      "finite polysquare translation surface",
      "adjacent atomic squares",
      "corresponding piecewise linear flow",
      "irreversible"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}