Multifractal dimensions for invariant subsets of piecewise monotonic interval maps

Volume 176 / 2003

Franz Hofbauer, Peter Raith, Thomas Steinberger Fundamenta Mathematicae 176 (2003), 209-232 MSC: 37E05, 37C45, 28A80, 37B40, 37A35, 28A78, 37D20. DOI: 10.4064/fm176-3-2

Abstract

The multifractal generalizations of Hausdorff dimension and packing dimension are investigated for an invariant subset $A$ of a piecewise monotonic map on the interval. Formulae for the multifractal dimension of an ergodic invariant measure, the essential multifractal dimension of $A$, and the multifractal Hausdorff dimension of $A$ are derived.

Authors

  • Franz HofbauerInstitut für Mathematik
    Universität Wien
    Strudlhofgasse 4
    A-1090 Wien, Austria
    e-mail
  • Peter RaithInstitut für Mathematik
    Universität Wien
    Strudlhofgasse 4
    A-1090 Wien, Austria
    e-mail
  • Thomas SteinbergerInstitut für Ökonometrie,
    Operations Research und Systemtheorie
    Technische Universität Wien
    Argentinierstraße 8
    A-1040 Wien, Austria
    e-mail

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