Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 149-174

ASSOUAD TYPE DIMENSIONS FOR SELF-AFFINE SPONGES

Jonathan M. Fraser and Douglas C. Howroyd

The University of St Andrews, School of Mathematics and Statistics
St Andrews, KY16 9SS; Scotland; jon.fraser32 'at' gmail.com

The University of St Andrews, School of Mathematics and Statistics
St Andrews, KY16 9SS; Scotland; douglas.howroyd 'at' gmail.com

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.

2010 Mathematics Subject Classification: Primary 28A80; Secondary 28A78, 37C45, 28C15.

Key words: Assouad dimension, lower dimension, self-affine set, doubling measure, weak tangent.

Reference to this article: J. M. Fraser and D. C. Howroyd: Assouad type dimensions for self-affine sponges. Ann. Acad. Sci. Fenn. Math. 42 (2017), 149-174.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4213