Assouad type dimensions for self-affine sponges

Jonathan M. Fraser, Douglas C. Howroyd

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    Abstract

    We study the Assouad and lower dimensions of self-affine sponges; the higher dimensional analogue of the planar self-affine carpets of Bedford and McMullen. Our techniques involve the weak tangents of Mackay and Tyson as well as regularity properties of doubling measures in the context studied by Bylund and Gudayol.
    Original languageEnglish
    JournalAnnales Academiae Scientiarum Fennicae Mathematica
    Early online date10 Jan 2017
    DOIs
    Publication statusPublished - 2017

    Keywords

    • math.MG
    • math.CA
    • math.DS
    • 28A80, 28A78, 37C45, 28C15

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