{
  "id": "math/0609695",
  "version": "v2",
  "published": "2006-09-25T14:53:56.000Z",
  "updated": "2008-06-04T18:41:37.000Z",
  "title": "Equilibrium Measures for Maps with Inducing Schemes",
  "authors": [
    "Yakov Pesin",
    "Samuel Senti"
  ],
  "journal": "J. Mod. Dyn. 2 (2008), no. 3, 397- 430",
  "doi": "10.3934/jmd.2008.2.397",
  "categories": [
    "math.DS"
  ],
  "abstract": "We introduce a class of continuous maps f of a compact metric space I admitting inducing schemes and describe the tower constructions associated with them. We then establish a thermodynamical formalism, i.e., describe a class of real-valued potential functions \\phi on I which admit unique equilibrium measures \\mu_\\phi minimizing the free energy for a certain class of measures. We also describe ergodic properties of equilibrium measures including decay of correlation and the Central Limit Theorem. Our results apply in particular to some one-dimensional unimodal and multimodal maps as well as to multidimensional nonuniformly hyperbolic maps admitting Young's tower. Examples of potential functions to which our theory applies include \\phi_t=-t\\log|df| with t\\in(t_0, t_1) for some t_0<1<t_1. In the particular case of S-unimodal maps we show that one can choose t_0<0 and that the class of measures under consideration comprises all invariant Borel probability measures. Thus our results establish existence and uniqueness of both the measure of maximal entropy (by a different method than Hofbauer) and the absolutely continuous invariant measure extending results by Bruin and Keller for the parameters under consideration.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-06-04T18:41:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D25",
      "37D35",
      "37D45",
      "37E05",
      "37E10"
    ],
    "keywords": [
      "equilibrium measures",
      "inducing schemes",
      "invariant measure extending results",
      "hyperbolic maps admitting youngs",
      "maps admitting youngs tower"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9695P"
    }
  }
}