{
  "id": "0905.2680",
  "version": "v2",
  "published": "2009-05-16T12:32:05.000Z",
  "updated": "2010-01-19T16:09:25.000Z",
  "title": "Lyapunov spectrum of asymptotically sub-additive potentials",
  "authors": [
    "De-Jun Feng",
    "Wen Hunag"
  ],
  "comment": "44 pages",
  "categories": [
    "math.DS",
    "math.CA"
  ],
  "abstract": "For general asymptotically sub-additive potentials (resp. asymptotically additive potentials) on general topological dynamical systems, we establish some variational relations between the topological entropy of the level sets of Lyapunov exponents, measure-theoretic entropies and topological pressures in this general situation. Most of our results are obtained without the assumption of the existence of unique equilibrium measures or the differentiability of pressure functions. Some examples are constructed to illustrate the irregularity and the complexity of multifractal behaviors in the sub-additive case and in the case that the entropy map that is not upper-semi continuous.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-01-19T16:09:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D35",
      "37C45"
    ],
    "keywords": [
      "lyapunov spectrum",
      "unique equilibrium measures",
      "entropy map",
      "general asymptotically sub-additive potentials",
      "lyapunov exponents"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00220-010-1031-x",
      "journal": "Communications in Mathematical Physics",
      "year": 2010,
      "month": "Jul",
      "volume": 297,
      "number": 1,
      "pages": 1
    },
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010CMaPh.297....1F"
    }
  }
}