{
  "id": "1403.7794",
  "version": "v2",
  "published": "2014-03-30T18:24:30.000Z",
  "updated": "2014-10-27T16:43:18.000Z",
  "title": "Unbounded Regime for Circle Maps with a Flat Interval",
  "authors": [
    "Liviana Palmisano"
  ],
  "comment": "\"Unbounded Regime for Circle Maps with a Flat Interval\" is accepted for publication in \"Discrete and Continuous Dynamical System - A\". Section 5 of the first version has been removed for scientific reasons. After extending it is now a separate paper at arXiv:1410.6269",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study C^2 weakly order preserving circle maps with a flat interval. In particular we are interested in the geometry of the mapping near to the singularities at the boundary of the flat interval. Without any assumption on the rotation number we show that the geometry is degenerate when the degree of the singularities is less than or equal to two and becomes bounded when the degree goes to three. As an example of application, the result is applied to study Cherry flows.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-30T18:24:30.000Z",
      "title": "Unbounded Regime for Circle Maps and Physical Measures for Cherry Flows",
      "abstract": "We study $C^2$ weakly order preserving circle maps with a flat interval. In particular we are interested in the geometry of the mapping near to the singularities at the boundary of the flat interval. Without any assumption on the rotation number we show that the geometry is degenerate when the degree of the singularities is less than or equal to two and become bounded when the degree goes to three. This result allows us to give a description of the physical measures on Cherry flows.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-27T16:43:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cherry flows",
      "physical measures",
      "unbounded regime",
      "flat interval",
      "weakly order preserving circle maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.7794P"
    }
  }
}