Assouad type dimensions for self-affine sponges

Jonathan M. Fraser; Douglas C. Howroyd

doi:10.5186/aasfm.2017.4213

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 language	English
Journal	Annales Academiae Scientiarum Fennicae Mathematica
Early online date	10 Jan 2017
DOIs	https://doi.org/10.5186/aasfm.2017.4213
Publication status	Published - 2017

Keywords

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

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10.5186/aasfm.2017.4213

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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.",

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Assouad type dimensions for self-affine sponges

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