Properties of Quasi-Assouad dimension
Abstract
The connections between quasi-Assouad dimension and tangents are studied. We apply these results to the calculation of the quasi-Assouad dimension for a class of planar self-affine sets. We also show that sets with decreasing gaps have quasi-Assouad dimension or and exhibit an example of a set in the plane whose quasi-Assouad dimension is smaller than that of its projection onto the -axis, showing that quasi-Assouad dimension may increase under Lipschitz mappings. Moreover, for closed sets, we show that the Hausdorff dimension is an upper bound for the lower-Assouad dimension.
Keywords
Cite
@article{arxiv.1703.02526,
title = {Properties of Quasi-Assouad dimension},
author = {Ignacio García and Kathryn Hare},
journal= {arXiv preprint arXiv:1703.02526},
year = {2019}
}
Comments
Theorem 1 and its consequences were removed because it proof was not correct. Added a Proposition showing that for closed sets, the Hausdorff dimension is an upper bound for the lower-quasi Assouad dimension