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

Andreas Anckar

    Research output: Contribution to journalArticleScientificpeer-review

    Abstract

    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.
    Original languageUndefined/Unknown
    Pages (from-to)853–864
    JournalJournal of Mathematical Analysis and Applications
    Volume440
    Issue number2
    DOIs
    Publication statusPublished - 2016
    MoE publication typeA1 Journal article-refereed

    Keywords

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

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