{
  "id": "1603.00591",
  "version": "v1",
  "published": "2016-03-02T06:29:46.000Z",
  "updated": "2016-03-02T06:29:46.000Z",
  "title": "Removal of phase transition of the Chebyshev quadratic and thermodynamics of Hénon-like maps near the first bifurcation",
  "authors": [
    "Hiroki Takahasi"
  ],
  "comment": "24 pages, 6 figures",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We treat a problem at the interface of dynamical systems and equilibrium statistical physics. It is well-known that the geometric pressure function $$t\\in\\mathbb R\\mapsto \\sup_{\\mu}\\left\\{h_\\mu(T_2)-t\\int\\log |dT_2(x)|d\\mu(x)\\right\\}$$ of the Chebyshev quadratic map $T_2(x)=1-2x^2$ $(x\\in\\mathbb R)$ is not differentiable at $t=-1$. We show that this phase transition can be \"removed\", by an arbitrarily small singular perturbation of the map $T_2$ into H\\'enon-like diffeomorphisms. A proof of this result relies on an elaboration of the well-known inducing techniques adapted to H\\'enon-like dynamics near the first bifurcation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-02T06:29:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D25",
      "37D35",
      "37G25",
      "82C26"
    ],
    "keywords": [
      "first bifurcation",
      "phase transition",
      "hénon-like maps",
      "thermodynamics",
      "chebyshev quadratic map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160300591T"
    }
  }
}