Assouad type dimensions for self-affine sponges
Metric Geometry
2017-03-30 v3 Classical Analysis and ODEs
Dynamical Systems
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.
Keywords
Cite
@article{arxiv.1508.03393,
title = {Assouad type dimensions for self-affine sponges},
author = {Jonathan M. Fraser and Douglas C. Howroyd},
journal= {arXiv preprint arXiv:1508.03393},
year = {2017}
}
Comments
29 pages, 6 figures. To appear in Ann. Acad. Sci. Fenn. Math