Assouad type dimensions for self-affine sponges

Jonathan M. Fraser, Douglas C. Howroyd

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    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
    Publication statusPublished - 2017


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


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