Dimension bounds for invariant measures of bi-Lipschitz iterated function systems

Andreas Anckar

    Tutkimustuotos: LehtiartikkeliArtikkelivertaisarvioitu

    Abstrakti

    We study probabilistic iterated function systems (IFSs), consisting of a finite or infinite number of average-contracting bi-Lipschitz maps on Rd. If our strong open set condition is also satisfied, we show that both upper and lower bounds for the Hausdorff and packing dimensions of the invariant measure can be found. Both bounds take on the familiar form of ratio of entropy to the Lyapunov exponent. Proving these bounds in this setting requires methods which are quite different from the standard methods used for average-contracting IFSs.
    AlkuperäiskieliEi tiedossa
    Sivut853–864
    JulkaisuJournal of Mathematical Analysis and Applications
    Vuosikerta440
    Numero2
    DOI - pysyväislinkit
    TilaJulkaistu - 2016
    OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

    Keywords

    • Iterated function systems
    • Fractals
    • Hausdorff dimension
    • invariant measures

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