{
  "id": "1208.5449",
  "version": "v1",
  "published": "2012-08-27T17:16:00.000Z",
  "updated": "2012-08-27T17:16:00.000Z",
  "title": "The Analyticity of a Generalized Ruelle's Operator",
  "authors": [
    "Eduardo Antonio da Silva",
    "Raderson Rodrigues da Silva",
    "Rafael Rigao Souza"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this work we propose a generalization of the concept of Ruelle operator for one dimensional lattices used in thermodynamic formalism and ergodic optimization, which we call generalized Ruelle operator, that generalizes both the Ruelle operator proposed in [BCLMS] and the Perron Frobenius operator defined in [Bowen]. We suppose the alphabet is given by a compact metric space, and consider a general a-priori measure to define the operator. We also consider the case where the set of symbols that can follow a given symbol of the alphabet depends on such symbol, which is an extension of the original concept of transition matrices from the theory of subshifts of finite type. We prove the analyticity of the Ruelle operator and present some examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-27T17:16:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A60",
      "37A50",
      "82B05"
    ],
    "keywords": [
      "generalized ruelles operator",
      "ruelle operator",
      "analyticity",
      "compact metric space",
      "general a-priori measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.5449D"
    }
  }
}